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The basic tool for studying the ageing and associated characteristics of any lifetime equipments is the reliability/survival function. It is common practice that while estimating the parameters of a model, one usually adopt maximum likelihood estimation method as the starting point as a classical method of estimation. In this paper, we consider maximum product of spacing estimation, besides using maximum likelihood method for estimating the reliability characteristics, such as, mean time to system failure (MTSF), reliability function (RF) and hazard rate function (HF) at a specified time point t 0 for logistic-exponential distribution. In addition, three bootstrap methods are considered for obtaining confidence intervals of MTSF, RT and HF. Besides, Bayesian estimation method is considered under symmetric as well as asymmetric loss functions using gamma priors for both shape and scale parameters for the considered model. Further, highest posterior density credible intervals are obtained by using a Markov chain Monte Carlo method with Gibbs sampler under Metropolis–Hastings sampling procedure. Average widths and coverage probabilities for each confidence intervals are computed. A Monte Carlo simulation study is carried out to compare the performance of the proposed estimates. Finally, two real data sets have been re-analyzed for illustrative purposes. [ABSTRACT FROM AUTHOR]

Abstract.The negative multinomial (NM) distribution is of interest in various application studies. Based on closed-form n-consistent estimators, new and fast closed-form efficient estimators are proposed for the NM distribution. The theorem applied to derive the new estimators guarantees two important properties of the new closed-form efficient estimators: asymptotic efficiency and normality. The new closed-form efficient estimators are denoted as MLE-CEs, because the asymptotic distribution is the same as that of the maximum likelihood estimators (MLEs). Simulation studies suggest that the MLE-CE performs similarly to its MLE. The estimated accuracies of the MLE and MLE-CE are generally better than the method of moments estimator (MME) for relatively large 풑 values. The MLE-CE is 10–30 times faster than the MLE, especially for large sample sizes, which is good for the big data era. Considering the estimated accuracy and computing time, the MLE-CE is recommended for large 풑 values, whereas the MME is recommended for other conditions. [ABSTRACT FROM AUTHOR]

AbstractIn this article, we investigate outlier observations in the Pareto distribution, by introducing two new tests: the generalized likelihood ratio and the uniformly most powerful tests for the outlier parameter of this distribution. Prior to this, we outline the necessary prerequisites for our study, including a model for outliers, the density function of the Pareto distribution in the presence of k outliers which is obtained from the same distribution, etc. Furthermore, we present joint probability density functions (conditional) and joint cumulative distribution functions (conditional) through several Lemmas and Corollaries. Then, using simulation study, we compare the power of our introduced tests against previously established for detecting outliers. Finally, we provide real examples to demonstrate the performance of these tests. [ABSTRACT FROM AUTHOR]

This paper introduces a new estimator for the Tobit regression model when the multicollinearity exists. This estimator is called almost unbiased Tobit Liu-Type estimator, which is obtained by a mixture between the Liu-Type estimator and almost unbiased estimator. This estimator avoids the negative effects of multicollinearity on the maximum likelihood estimator. Furthermore, we check the superiority of the new estimator over the maximum likelihood estimator, Liu-Type estimator and almost unbiased estimator according to the simulated mean square error SMSE criteria. In addition, we run the simulation study to investigate the effects of a group of factors on the performance of the new estimator. Finally, to check the benefits of the new estimator via the real data, we use two applications for the Tobit regression, the English Premier League data and Egyptian agricultural GDP data. [ABSTRACT FROM AUTHOR]

AbstractModeling with the gamma regression model is common when the dependent variable is positively skewed and follows a gamma distribution. The maximum likelihood (ML) estimator is used to estimate the parameters for this model. However, when there is multicollinearity, the ML estimator is inefficient. As a result, we propose a new improved gamma (NIG) estimator for this model’s parameter estimation in the presence of multicollinearity. Theoretical comparisons of the NIG estimator with some existing gamma estimators are done via mean squared error. Additionally, a real-data example and a simulation study are conducted to provide a clear view of the NIG estimator’s superior performance over other available ones. The results show that the NIG estimator outperforms previous gamma estimators in terms of mean squared error. [ABSTRACT FROM AUTHOR]

The Quadratic Transmuted Generalized Exponential Distribution (QTGED) enhances the generalized exponential distribution, making it a significant development for handling complex decision-making contexts. Traditional statistical distributions often focus on representing degrees of truth or membership in fuzzy sets, yet they struggle to capture situations involving incomplete, vague, or contradictory data accurately. This study introduces the Neutrosophic Quadratic Transmuted Generalized Exponential Distribution (NQTGED), specifically designed to address indeterminacy and transmuted data. Neutrosophic theory is essential here, as it overcomes the limitations of classical and fuzzy set theories by effectively managing uncertainty, indeterminacy, and inconsistency in data. By simultaneously representing truth, indeterminacy, and falsity, neutrosophic sets offer a comprehensive framework for modeling uncertainty. Traditional distributions lack the adaptability needed for evolving data complexities, often falling short when faced with non-standard data distributions or outliers. Addressing these challenges requires innovative approaches that incorporate advanced mathematical models for uncertainty. This is especially valuable in real-world situations, where data is frequently incomplete, imprecise, or contradictory, and sometimes transmuted. The study derives various mathematical properties of the model, assesses parameter estimation using maximum likelihood and simulation, and demonstrates practical applications with cancer remission data. Simulation results reveal that Neutrosophic Average Biases (NABs) and Neutrosophic Mean Square Errors (NMSEs) decrease as sample sizes increase, indicating strong and accurate parameter estimation. NQTGED provides superior fit and performance, offering significant insights for applications in reliability engineering and biomedical sciences. [ABSTRACT FROM AUTHOR]

The mixed model with polynomial drift of the form $X(t)=\theta \mathcal{P}(t)+\alpha W(t)+\sigma {B_{H}^{n}}(t)$ is studied, where ${B_{H}^{n}}$ is the nth-order fractional Brownian motion with Hurst index $H\in (n-1,n)$ and $n\ge 2$, independent of the Wiener process W. The polynomial function $\mathcal{P}$ is known, with degree $d(\mathcal{P})\in [1,n)$. Based on discrete observations and using the ergodic theorem estimates of H, ${\alpha ^{2}}$ and ${\sigma ^{2}}$ are given. Finally, a continuous time maximum likelihood estimator of θ is provided. Both strong consistency and asymptotic normality of the proposed estimators are established.

Reference intervals are indispensable for the interpretation of medical laboratory results to distinguish “normal” from “pathological” values. Recently, indirect methods have been published, which estimate reference intervals from a mixture of normal and pathological values based on certain statistical assumptions on the distribution of the values from the healthy population. Some analytes face the problem that a significant proportion of the measurements are below the limit of detection (LOD), meaning that there are no quantitative data for these values, only the information that they are smaller than the LOD. Standard statistical methods for reference interval estimation are not designed to incorporate values below the LOD. We propose two variants of the indirect method reflimR—a quantile- and maximum likelihood-based estimator—that are able to cope with values below the LOD. We show, based on theoretical analyses, simulation experiments, and real data, that our approach yields good estimates for the reference interval, even when the values below the LOD contribute a substantial proportion to the data.

This study takes into account the efficient estimation of the probability density function (PDF) of the Weibull-Burr XII distribution and the cumulative distribution function (CDF), which allows for greater flexibility than many other generalized distributions in use today. Nine traditional estimators are used to produce the analytical formulations for the bias and the mean squared error (MSE). A simulated investigation is conducted to evaluate the finite sample performance of the suggested estimators in terms of MSE values. In addition to that a real data application is also demonstrated for illustration.

The current research is concerned with double stage shrunken technique in order to estimate the shape parameter (Burr XII) distribution, when previous knowledge regarding the value shape is available as the original estimate. The formulas for the Relative efficiency, mean squared error, and bias ratio are derived, For the aforementioned expressions, numerical results and conclusions were shown. [ABSTRACT FROM AUTHOR]

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Reference intervals are indispensable for the interpretation of medical laboratory results to distinguish "normal" from "pathological" values. Recently, indirect methods have been published, which estimate reference intervals from a mixture of normal and pathological values based on certain statistical assumptions on the distribution of the values from the healthy population. Some analytes face the problem that a significant proportion of the measurements are below the limit of detection ( LOD ), meaning that there are no quantitative data for these values, only the information that they are smaller than the LOD . Standard statistical methods for reference interval estimation are not designed to incorporate values below the LOD . We propose two variants of the indirect method reflimR—a quantile- and maximum likelihood-based estimator—that are able to cope with values below the LOD . We show, based on theoretical analyses, simulation experiments, and real data, that our approach yields good estimates for the reference interval, even when the values below the LOD contribute a substantial proportion to the data. [ABSTRACT FROM AUTHOR]

Parameter estimation of stochastic differential equation has recently been discussed by many authors. The aim of this paper is to study the rates of convergence of approximate maximum likelihood estimator. More precisely, for Markovian switching diffusions, we first show the convergence rates of the continuous maximum likelihood estimator under the Lipschitz conditions. Then we also discuss the probabilistic bounds on |θn;T - θT| under the non-Lipschitz conditions. [ABSTRACT FROM AUTHOR]

For a truncated family of distributions with a truncation parameter γ and a parameter θ as a nuisance parameter, we derive the stochastic expansions of bias-adjusted maximum likelihood estimators γ ̂ M L ∗ θ and γ ̂ M L ∗ of γ based on a sample of size n when θ is known and when θ is unknown, respectively. The asymptotic loss of γ ̂ M L ∗ relative to γ ̂ M L ∗ θ is obtained up to the second order, that is the order n−1. The results are a generalization of those for a one-sided truncated exponential family of distributions. Its application to truncated t-distributions is also given. [ABSTRACT FROM AUTHOR]

This paper introduces a novel approach that combines symbolic data analysis with matrix theory through the concept of interval-valued random matrices. This framework is designed to address the complexities of real-world data, offering enhanced statistical modeling techniques particularly suited for large and complex datasets where traditional methods may be inadequate. We develop both frequentist and Bayesian methods for the statistical inference of interval-valued random matrices, providing a comprehensive analytical framework. We conduct extensive simulations to compare the performance of these methods, demonstrating that Bayesian estimators outperform maximum likelihood estimators under the Frobenius norm loss function. The practical utility of our approach is further illustrated through an application to climatology and temperature data, highlighting the advantages of interval-valued random matrices in real-world scenarios. [ABSTRACT FROM AUTHOR]

This paper elucidates the prerequisites for maximum likelihood estimation (MLE) of parameters within the exponential and scale parameter families. Estimation of these parameters is predicated on data derived from censored samples and seeks to adhere to stochastic ordering principles. The study establishes that for two independent normal distributions and a two-parameter exponential distribution discernible by the distinct parameter sets, the MLEs of the parameters evince a stochastically ordered relationship when evaluated using full datasets. Furthermore, this research is extended to corroborate the persistence of stochastic ordering in the MLEs of such parameters under conditions of fixed censoring of samples. [ABSTRACT FROM AUTHOR]

In this article, a new lifetime distribution named "inverse Ishita" with one parameter for modelling lifetime data is presented as a good alternative to known one-parameter distributions. Moreover, two types of estimation: point estimation and interval estimation are used to estimate the unknown parameter. Furthermore, numerical simulation is conducted to evaluate the performance of estimates at different parameter values and different sample sizes. Ultimately, to illustrate the flexibility and efficiency of the distribution, it was applied to a set of data and compared to the Weibull and Shanker distributions. It was found that the inverse Ishita distribution was a better fit for the data than the other distributions. [ABSTRACT FROM AUTHOR]

This study takes into account the efficient estimation of the probability density function (PDF) of the Weibull-Burr XII distribution and the cumulative distribution function (CDF), which allows for greater flexibility than many other generalized distributions in use today. Nine traditional estimators are used to produce the analytical formulations for the bias and the mean squared error (MSE). A simulated investigation is conducted to evaluate the finite sample performance of the suggested estimators in terms of MSE values. In addition to that a real data application is also demonstrated for illustration. [ABSTRACT FROM AUTHOR]

In analysis of survival data, the Accelerated Life Model (ALM) is one of the widely used semiparametric models, and we often encounter various types of censored survival data, such as right censored data, doubly censored data, interval censored data, partly interval-censored data, etc. For complicated types of censored data, the studies of statistical inferences on the ALM are very technical and challenging mathematically, thus up to now little work has been done. In this article, we extend the concept of weighted empirical likelihood (WEL) from univariate case to multivariate case, and we apply it to the ALM, which leads to an estimation approach, called weighted maximum likelihood estimator, as well as the WEL based confidence interval for the regression parameter. Our proposed procedures are applicable to various types of censored data under a unified framework, and some simulation results are presented.

AbstractThis study focuses on parameter estimation in the presence of multicollinearity for the count response that follows the Waring distribution. The Waring regression model deals with over-dispersion. So, this study proposed the Waring ridge regression (WRR) model as a solution for multicollinearity with over-dispersion. We conducted a theoretical comparison between the ridge estimator and the maximum likelihood estimators using matrix and scalar mean squared error as a performance evaluation criterion. Several ridge parameters are considered for the WRR estimator. The performance of these parameters is numerically evaluated using a Monte Carlo simulation study and a real application. The results of the simulation and application demonstrate the superiority of the WRR model with different ridge parameters over the maximum likelihood estimator. [ABSTRACT FROM AUTHOR]

One new factor driving the banking industry towards long-term, high-quality growth is digital marketing, which has arisen within the framework of the digital economy. The purpose of this research is to examine the effect of digital marketing on the financial results of MENA banks from 2010 to 2023. The research examines the impact of digital marketing techniques on the effectiveness of financial institutions through Tobit regression analysis, taking into account and controlling for sustainable practices (ESG), bank-specific characteristics (capital adequacy, bank size, liquidity, and cost efficiency), and macroeconomic variables (GDP and inflation). This empirical paper managed to collect the data for eleven countries in the MENA from the Refinitiv Eikon platform, world bank database, and the annual reports of relevant banks in the different stock markets. The final sample included 78 banks out of 120 listed banks. The results show that there is a clear association between the presence of digital marketing campaigns and improved profitability and market share growth for banks. Aligning digital initiatives with ESG principles is crucial for long-term value development, and sustainable practices increase these beneficial benefits even more. The research also shows that macroeconomic factors and bank-specific characteristics affect how effective digital marketing campaigns are. The significance of digital transformation and ESG integration in promoting competitive advantages and long-term growth in the MENA banking sector is highlighted by these findings, which have important implications for policy, investors, and bank executives. [ABSTRACT FROM AUTHOR]

In this article we, proposed a new two parameter distribution called inverted power modified Lindley distribution. The main objective is to introduce an extension to inverted modified Lindley distribution as an alternative to the inverted exponential, inverted gamma and inverted modified Lindley distributions, respectively. The proposed distribution is more flexible than the above mentioned distributions in terms of its hazard rate function. In the part of estimation of the proposed model, we first utilize the maximum likelihood (ML) estimator and parametric bootstrap confidence intervals, viz., standard bootstrap, percentile bootstrap, bias-corrected percentile (BCPB), bias-corrected accelerated bootstrap (BCAB) from the classical point of view as well the Bayesian estimation under different loss functions, squared error loss function, modified squared error loss function, and Bayes credible interval as to obtain the model parameter based on order statistics. A simulation study is carried out to check the efficiency of the classical and the Bayes estimators in terms of mean squared errors and posterior risks, respectively. Two real life data sets, have been analyzed for order statistics to demonstrate how the proposed methods may work in practice. [ABSTRACT FROM AUTHOR]

When the weight function depends on the lengths of the units of interest, the resulting distribution is called length biased. Length biased distribution is thus a special case of the more general form, known as weighted distribution. In this study, we introduce a novel probability distribution named the Length-Biased Sabur distribution (LBSD). This new distribution enhances the traditional Sabur distribution by incorporating a weighted transformation approach. The paper investigates the probability density function (pdf) and the cumulative distribution function (cdf) associated with the LBSD. A thorough examination of the distinctive structural properties of the proposed model is conducted, covering the survival function, conditional survival function, hazard function, cumulative hazard function, mean residual life, moments, moment generating function, characteristic function, likelihood ratio test, ordered statistics, entropy measures, and Bonferroni and Lorenz curve. [ABSTRACT FROM AUTHOR]

Being an important probability distribution with moderate skewness, the two-parameter gamma distribution is widely used in statistics. However, the maximum likelihood estimators (MLEs) of its parameters do not have closed forms, making them difficult to be implemented in applications. Moreover, the MLE of its shape parameter has low estimation efficiency due to its considerable bias. Thus, many other estimators have been investigated in the literature. We propose an easy computation of the MLEs in this article, where the MLE of the shape parameter is modified to be highly efficient and significantly better than most of existing estimators. [ABSTRACT FROM AUTHOR]

In many manufacturing industries, the lifetime performance index C L is utilized to assess the manufacturing process performance for products following some lifetime distributions and subjecting them to progressive type I interval censoring. This paper aims to explore the sampling design required to achieve a specified level of significance and test power for products with lifetimes following the Exponentiated Frech'et distribution. Since lifetime distribution is an asymmetrical probability distribution, this investigation is related to the topic of asymmetrical probability distributions and applications in various fields. When the termination time is fixed but the number of intervals is variable, the optimal number of inspection intervals and sample sizes yielding the minimized total experimental costs are determined and tabulated. When the termination time is varying, the optimal number of inspection intervals, sample sizes, and equal interval lengths achieving the minimum total experimental costs are determined and tabulated. Optimal parameter values are displayed in tabular form for feasible applications for users. Additionally, a practical example is provided to illustrate how this sampling design can be used to collect data by using the optimal setup of parameters, followed by a testing procedure to assess the capability of the production process. [ABSTRACT FROM AUTHOR]

We establish the exponential nonuniform Berry–Esseen bound for the maximum likelihood estimator of unknown drift parameter in an ultraspherical Jacobi process using the change of measure method and precise asymptotic analysis techniques. As applications, the optimal uniform Berry–Esseen bound and optimal Cramér-type moderate deviation for the corresponding maximum likelihood estimator are obtained. [ABSTRACT FROM AUTHOR]

In this paper, we have presented a novel extension of the Erlang-Truncated Exponential distribution (ETE), called Weighted Erland-Truncated Exponential distribution (WETE), and inspected its statistical properties and application to the system reliability. We calculated the parameters estimation and the Fishers information matrix, which are important for estimating various system component reliabilities. To validate the effectiveness of WETE distribution, the performance comparisons were made using real-life data sets from earthquakes, engineering, and medical sciences. The WETE distribution provides a better fit than other existing distributions. In the context of system reliability, the probability of a system or component functioning well is shown. We have used simulations to predict a system's performance under different conditions. The results show that the maximum likelihood estimator's performance improves consistency with large sample sizes in the WETE distribution. Finally, we have discussed the application of WETE in reliability optimization problems. The optimal allocation of reliabilities components is determined using the Lagrange multiplier technique. The effectiveness of reliability optimization is evident in improved system performance. This paper also studied the structural properties of WETE, such as the likelihood ratio test, Renyi and Tsallis entropies, order statistics, and Bonferroni and Lorenz curves. [ABSTRACT FROM AUTHOR]

Generalized Rayleigh, a weighted version of power Rayleigh distribution is introduced. The hazard function is increasing upon the values of parameters. The generalized model has been compared with different models for flexibility and efficiency using real life data sets. Further, the parameters of the new model are estimated via classical method of estimation. It is observed that weighted power Rayleigh distribution fits better than power Rayleigh, Rayleigh and weighted Rayleigh distributions. [ABSTRACT FROM AUTHOR]

In analysis of survival data, the Accelerated Life Model (ALM) is one of the widely used semiparametric models, and we often encounter various types of censored survival data, such as right censored data, doubly censored data, interval censored data, partly interval-censored data, etc. For complicated types of censored data, the studies of statistical inferences on the ALM are very technical and challenging mathematically, thus up to now little work has been done. In this article, we extend the concept of weighted empirical likelihood (WEL) from univariate case to multivariate case, and we apply it to the ALM, which leads to an estimation approach, called weighted maximum likelihood estimator, as well as the WEL based confidence interval for the regression parameter. Our proposed procedures are applicable to various types of censored data under a unified framework, and some simulation results are presented. [ABSTRACT FROM AUTHOR]

The present study aims primarily to address the issue of estimating the delay parameters in a dynamical system that is subjected to small noise, using the maximum likelihood method. Our investigation focuses mainly on the asymptotic properties, namely consistency, asymptotic normality, and asymptotic efficiency, of the estimator utilized. [ABSTRACT FROM AUTHOR]

Up to now, almost all existing methods for joint modeling survival data and longitudinal data rely on parametric/semiparametric assumptions on longitudinal covariate process, and the resulting inferences critically depend on the validity of these assumptions that are difficult to verify in practice. The kernel method-based procedures rely on choices of kernel function and bandwidth, and none of the existing methods provides estimate for the baseline distribution in proportional hazards model. This article proposes a proportional hazards model for joint modeling right censored survival data and intensive longitudinal data taking into account of within-subject historic change patterns. Without any parametric/semiparametric assumptions or use of kernel method, we derive empirical likelihood-based maximum likelihood estimators and partial likelihood estimators for the regression parameter and the baseline distribution function. We develop stable computing algorithms and present some simulation results. Analyses of real dataset are conducted for smoking cessation data and liver disease data. [ABSTRACT FROM AUTHOR]

The lifetime performance index is commonly used in the manufacturing industry to evaluate the performance of the capabilities of the production process. For products with multiple components, the comprehensive lifetime performance index, which is a monotonically increasing function of the overall process yield, is used to relate to each individual lifetime performance index. For products where the lifetime of the ith component follows an exponentiated Fréchet lifetime distribution, we examine the maximum likelihood estimators for both the comprehensive and individual lifetime performance indices based on the progressive type I interval-censored samples, deriving their asymptotic distributions. By specifying the target level for the comprehensive lifetime performance index, we can set the desired level for individual indices. A testing procedure, using the maximum likelihood estimator as the test statistic, was developed to determine if the comprehensive lifetime performance index meets the target. Given that the lifetime distribution is asymmetric, this study pertains to asymmetrical probability distributions and their applications across diverse fields. We illustrate the power analysis of this testing procedure with figures and summarize key findings. Finally, we demonstrate the application of this testing algorithm with a practical example involving two components to verify if the overall production process achieves the assigned target level. [ABSTRACT FROM AUTHOR]

In some real-life situations, we will face restrictions of time and sample size which cause a researcher to not have access to all of the data. Therefore, it is valuable to study the estimation of parameters based on information of available data. In such situations, using appropriate sampling schemes, to more efficient estimators are important. The aim of the present paper is to study the Bayes estimators of parameters of the Pareto type-I model under different loss functions and compare among them as well as with the classical estimator named maximum likelihood estimator based on upper record ranked set sampling scheme. Here the informative Gamma prior is used as the conjugate prior distribution for finding the Bayes estimator. We also used symmetric loss functions such as squared error loss function and asymmetric loss functions such as linear-exponential loss function. We present the analysis of a Monte Carlo simulation to compare the performance of the estimators with respect to their risks (average loss over sample space) based on upper record ranked set sampling. Finally, one real data set is analyzed to illustrate the performance of the proposed estimators. [ABSTRACT FROM AUTHOR]

In this paper, we used the maximum likelihood estimation (MLE) and the Bayes methods to perform estimation procedures for the reliability of stress-strength R = P(Y < X) based on independent adaptive progressive censored samples that were taken from the Chen distribution. An approximate confidence interval of R was constructed using a variety of classical techniques, such as the normal approximation of the MLE, the normal approximation of the log-transformed MLE, and the percentile bootstrap (Boot-p) procedure. Additionally, the asymptotic distribution theory and delta approach were used to generate the approximate confidence interval. Further, the Bayesian estimation of R was obtained based on the balanced loss function, which came in two versions here, the symmetric balanced squared error (BSE) loss function and the asymmetric balanced linear exponential (BLINEX) loss function. When estimating R using the Bayesian approach, all the unknown parameters of the Chen distribution were assumed to be independently distributed and to have informative gamma priors. Additionally, a mixture of Gibbs sampling algorithm and Metropolis-Hastings algorithm was used to compute the Bayes estimate of R and the associated highest posterior density credible interval. In the end, simulation research was used to assess the general overall performance of the proposed estimators and a real dataset was provided to exemplify the theoretical results. [ABSTRACT FROM AUTHOR]

The article deals with numerical estimation of the drift parameter in the continuous-time linear model with two independent fractional Brownian motions. The main focus is given to the computational difficulties of the maximum likelihood approach, in particular, to the construction of the approximate solution to the Fredholm integral equation of the second kind with a singular kernel. We also introduce two alternative estimators and investigate their asymptotic properties. The performance of all estimators is studied numerically. [ABSTRACT FROM AUTHOR]

This paper proposes a bootstrap testing approach based on an approximate maximum likelihood method to discern whether a diffusion process is linear or whether there are threshold effects in the drift, the diffusion term or in both. It complements an alternative method based on the least-squares estimator which focuses on threshold effects in the drift. Monte Carlo simulations illustrate that the proposed testing approach is able to detect the source of the non-linearity. Two empirical applications show the importance of modeling threshold effects in the diffusion instead of the drift. [ABSTRACT FROM AUTHOR]

In this study, we obtain relations for the moments of order statistics from the modified Lindley distribution without any restriction for the parameter. In addition, we use these moments to obtain the mean, variances, and covariances of order statistics from the modified Lindley distribution. In particular, we compare, through simulation study, the performance of the maximum likelihood estimation, ordinary and weighted least-squares estimation, percentile estimators, and Cramér–von Mises estimators. Finally, we apply the paper's findings to some real data sets. [ABSTRACT FROM AUTHOR]

Based on a progressive first-failure censoring (PFFC) sample, we discuss the statistical inferences of the entropy of a Rayleigh distribution. In particular, the Maximum likelihood and the different Bayes estimates for entropy are derived and compared via a Monte Carlo simulation study. Bayes estimators are developed using both symmetric and asymmetric loss functions. Approximate confidence intervals (CIs) and credible intervals (CrIs) of the entropy of the model are also performed. Numerical examples and a real data set are given to illustrate the proposed estimators. [ABSTRACT FROM AUTHOR]

The article offers a method for estimating the volatility covariance matrix of vectors of financial time series data using a change point approach. The proposed method supersedes general varying-coefficient parametric models, such as GARCH, whose coefficients may vary with time, by a change point model. In this study, an adaptive pointwise selection of homogeneous segments with a given right-end point by a local change point analysis is introduced. Sufficient conditions are obtained under which the maximum likelihood process is adaptive against the covariance estimate to yield an optimal rate of convergence with respect to the change size. This rate is preserved while allowing the jump size to diminish. Under these circumstances, argmax results of a two-sided negative Brownian motion or a two-sided negative drift random walk under vanishing and non-vanishing jump size regimes, respectively, provide inference for the change point parameter. Theoretical results are supported by the Monte–Carlo simulation study. A bivariate data on daily log returns of two US stock market indices as well as tri-variate data on daily log returns of three banks are analyzed by constructing confidence interval estimates for multiple change points that have been identified previously for each of the two data sets. [ABSTRACT FROM AUTHOR]