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This article proposes a new extension of the inverse Weibull distribution called, logarithmic transformed inverse Weibull distribution which can provide better fits than some of its well-known extensions. The proposed distribution contains inverse Weibull, inverse Rayleigh, inverse exponential, logarithmic transformed inverse Rayleigh and logarithmic transformed inverse exponential distributions as special sub-models. Our main focus is to derive some of its mathematical properties along with the estimation of its unknown parameters using frequentist and Bayesian estimation methods. We compare the performances of the proposed estimators using extensive numerical simulations for both small and large samples. The importance and potentiality of this distribution is analyzed via two real data sets. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to discuss a general family of distributions generated from the symmetrical arcsine distribution. The considered family includes various asymmetrical and symmetrical probability distributions as special cases. A particular case of a symmetrical probability distribution from this family is the Arcsine-Gaussian distribution. Key statistical properties of this distribution including quantile, mean residual life, order statistics and moments are derived. The Arcsine-Gaussian parameters are estimated using two classical estimation methods called moments and maximum likelihood methods. A simulation study which provides asymptotic distribution of all considered point estimators, 90% and 95% asymptotic confidence intervals are performed to examine the estimation efficiency of the considered methods numerically. The simulation results show that both biases and variances of the estimators tend to zero as the sample size increases, i.e., the estimators are asymptotically consistent. Also, when the sample size increases the coverage probabilities of the confidence intervals increase to the nominal levels, while the corresponding length decrease and approach zero. Two real data sets from the medicine filed are used to illustrate the flexibility of the Arcsine-Gaussian distribution as compared with the normal, logistic, and Cauchy models. The proposed distribution is very versatile to fit real applications and can be used as a good alternative to the traditional gaussian distribution. [ABSTRACT FROM AUTHOR]

The current epidemic outbreak COVID-19 first took place in the Wuhan city of China and then spread worldwide. This deadly disease affected millions of people and compelled the governments and other concerned institutions to take serious actions. Around 0.28 million people have died from the COVID-19 outbreak as of May 11, 2020, 05:41 GMT, and the number is still increasing exponentially. The results of any scientific investigation of this phenomenon are still to come. However, now it is urgently needed to evaluate and compare the disease dynamics to improve the quarantine activities and the level of individual protection, to at least speed up the rate of isolation of infected persons. In the domain of big data science and other related areas, it is always of interest to provide the best description of the data under consideration. Therefore, in this article, we compare the COVID-19 pandemic dynamics between two neighboring Asian countries, Iran and Pakistan, to provide a framework to arrange the appropriate quarantine activities. Simple tools for comparing this deadly pandemic dynamic have been presented that can be adopted to produce the bases for inferences. Most importantly, a new statistical model is developed to provide the best description of COVID-19 daily deaths data in Iran and Pakistan. [ABSTRACT FROM AUTHOR]

We study a new continuous distribution called the Marshall-Olkin modified Burr III distribution. The density function of the proposed model can be expressed as a mixture of modified Burr III densities. A comprehensive account of its mathematical properties is derived. The model parameters are estimated by the method of maximum likelihood. The usefulness of the derived model is illustrated over other distributions using a real data set. [ABSTRACT FROM AUTHOR]

We introduce the Kumaraswamy alpha power-G (KAP-G) family which extends the alpha power family (Mahdavi and Kundu, 2017) and some other families. We consider the Weibull as baseline for the KAP family and generate Kumaraswamy alpha power Weibull distribution which has right-skewed, left-skewed, symmetrical, and reversed-J shaped densities, and decreasing, increasing, bathtub, upside-down bathtub, increasing-decreasing–increasing, J shaped and reversed-J shaped hazard rates. The proposed distribution can model non-monotone and monotone failure rates which are quite common in engineering and reliability studies. Some basic mathematical properties of the new model are derived. The maximum likelihood estimation method is used to evaluate the parameters and the observed information matrix is determined. The performance and flexibility of the proposed family is illustrated via two real data applications. [ABSTRACT FROM AUTHOR]

We introduce a new three-parameter model called the odd inverse Pareto exponential distribution which extends the exponential distribution and provides constant, decreasing, increasing, decreasing-increasing, upside-down bathtub and bathtub failure rate shapes. Some of its mathematical properties are derived. The maximum likelihood method is used to estimate the model parameters. The proposed model provides better fits over some existing distributions by means of two real data sets. [ABSTRACT FROM AUTHOR]

A new family of distributions called type II exponentiated half logistic is introduced. Four new special models are presented. Some mathematical properties of the new family are derived including explicit expressions for the quantile function, moments, probability weighted moments, mean deviation, order statistics and Rényi entropy. Parameter estimation of the proposed family are explored by the maximum likelihood. Two real data sets are employed to show the usefulness of the new family. [ABSTRACT FROM AUTHOR]

This paper introduces a new four-parameter lifetime model called the Marshall-Olkin generalized Burr XII (MOGBXII) distribution. We derive some of its mathematical properties, including quantile and generating functions, ordinary and incomplete moments, mean residual life, and mean waiting time and order statistics. The MOGBXII density can be expressed as a linear mixture of Burr XII densities. The maximum likelihood and least squares methods are used to estimate the MOGBXII parameters. Simulation results are obtained to compare the performances of the two estimation methods for both small and large samples. We empirically illustrate the flexibility and importance of the MOGBXII distribution in modeling various types of lifetime data. [ABSTRACT FROM AUTHOR]

We study a new family of distributions defined by the minimum of the Poisson random number of independent identically distributed random variables having a general Weibull-G distribution (see Bourguignon et al. (2014)). Some mathematical properties of the new family including ordinary and incomplete moments, quantile and generating functions, mean deviations, order statistics, reliability and entropies are derived. Maximum likelihood estimation of the model parameters is investigated. Three special models of the new family are discussed. We perform three applications to real data sets to show the potentiality of the proposed family. [ABSTRACT FROM AUTHOR]

We introduce a new class of distributions called the Weibull Marshall–Olkin-G family. We obtain some of its mathematical properties. The special models of this family provide bathtub-shaped, decreasing-increasing, increasing-decreasing-increasing, decreasing-increasing-decreasing, monotone, unimodal and bimodal hazard functions. The maximum likelihood method is adopted for estimating the model parameters. We assess the performance of the maximum likelihood estimators by means of two simulation studies. We also propose a new family of linear regression models for censored and uncensored data. The flexibility and importance of the proposed models are illustrated by means of three real data sets. [ABSTRACT FROM AUTHOR]

In this paper, a comparison between the life distribution of a new unit with that of a used unit in the increasing convex order is made leading to a new class of life distributions which we call "new better than used in convex ordering of second order". This class includes as subclasses the NBU and the NBUC and is a subclass of the NBUCA class. Preservation properties under convolution, random maxima, mixing and formation of coherent structures are established. Stochastic comparisons of the excess lifetime when the inter-arrival times belong to the NBUC(2) class are developed. Some applications of Poisson shock models and a test of exponentiality against NBUC(2) alternative are presented. [ABSTRACT FROM AUTHOR]

We introduce a new family of continuous distributions called the odd inverse Pareto-G class which extends the exponentiated- G family due to Gupta et al. [R. C. Gupta, P. L. Gupta, R. D. Gupta, Comm. Statist. Theory Methods, 27 (1998), 887-904] and the Marshall-Olkin-G class due to Marshall and Olkin [A. W. Marshall, I. Olkin, Biometrika, 84 (1997), 641-652]. We define and study two special models of the proposed family which are capable of modeling various shapes of aging and failure criteria. The special models of this family can provide reversed J-shape, symmetric, left skewed, right skewed, unimodal or bimodal shapes for the density function. Some of its mathematical properties are derived. The maximum likelihood method is used to estimate the model parameters. By means of four real data sets we show that the special models of this family have superior performance over several existing distributions. [ABSTRACT FROM AUTHOR]

This paper introduces a new family of continuous distributions called the transmuted transmuted-G family which extends the quadratic rank transmutation map pioneered by Shaw and Buckley [W. T. Shaw, I. R. Buckley, arXiv preprint, 2007 (2007), 28 pages]. We provide two special models of the new family which can be used effectively to model survival data since they accommodate increasing, decreasing, unimodal, bathtub-shaped and increasing-decreasing-increasing hazard functions. We also provide two new characterization theorems of the proposed family. The estimation of the model parameters is performed by the maximum likelihood method. The flexibility of the proposed family is illustrated by means of two applications to real data. [ABSTRACT FROM AUTHOR]

The inactivity time, also known as reversed residual life, has been a topic of increasing interest in the literature. In this investigation, based on the comparison of inactivity times of two devices, we introduce and study a new estimate of the probability of the inactivity time of one device exceeding that of another device. The problem studied in this paper is important for engineers and system designers. It would enable them to compare the inactivity times of the products and, hence to design better products. Several properties of this probability are established. Connections between the target probability and the reversed hazard rates of the two devices are established. In addition, some of the reliability properties of the new concept are investigated extending the well-known probability ordering. Finally, to illustrate the introduced concepts, many examples and applications in the context of reliability theory are included. [ABSTRACT FROM AUTHOR]

In this paper, we define and study a four-parameter model called the transmuted Burr XII distribution. We obtain some of its mathematical properties including explicit expressions for the ordinary and incomplete moments, generating function, order statistics, probability weighted moments and entropies. We formulate and develop a log-linear model using the new distribution so-called the log-transmuted Burr XII distribution for modeling data with a unimodal failure rate function, as an alternative to the log-McDonald Burr XII, log-beta Burr XII, log-Kumaraswamy Burr XII, log-Burr XII and logistic regression models. The flexibility of the proposed models is illustrated by means of three applications to real data sets. [ABSTRACT FROM AUTHOR]

In this paper, a new three-parameter Pareto distribution is introduced and studied. We discuss various mathematical and statistical properties of the new model. Some estimation methods of the model parameters are performed. Moreover, the peaks-over-threshold method is used to estimate Value-at-Risk (VaR) by means of the proposed distribution. We compare the distribution with a few other models to show its versatility in modelling data with heavy tails. VaR estimation with the Burr X Pareto distribution is presented using time series data and the new model could be considered as an alternative VaR model against the generalized Pareto model for financial institutions. [ABSTRACT FROM AUTHOR]