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To define useful numbers having values from 0 to 1, as percentages, probabilities, and proportions, the unit probability models are often employed in probability and statistics. In this paper, a new two-parameter model on the unit interval, entitled the unit Mirra distribution (UMD) is suggested which is a modification of the Mirra distribution (MD). Various statistical properties of the proposed UMD as the r th moment, variance, inverse moments, and incomplete moments are presented. Also, the distributions of order statistics, coefficients of variation and skewness, stochastics ordering, and median and mean deviations are provided. The reliability functions such the hazard function, survival function, odds function, reversed hazard rate function, and the mean residual function are provided with supported graphical representation. The Lorenz curve, Gini index, and Bonferroni curve of the UMD with some simulations are included. The distribution parameters are estimated based on the maximum likelihood estimation, ordinary least squares estimation, Anderson-Darling and maximum product of spacing's estimation. Finally, two different applications of actual data sets that represent the times to infection of kidney dialysis patients in months and the trade share data on unit interval are carried out to evaluate the model's performance as compared to some competitors. It turns out that the suggested UMD can serve as a good alternative for modeling these data sets. [ABSTRACT FROM AUTHOR]

This paper introduces a modified form of the inverse Lomax distribution which offers more flexibility for modeling lifetime data. The new three-parameter model is provided as a member of the truncated Lomax-G procedure. The new modified distribution is called the truncated Lomax inverse Lomax distribution. The density of the new model can be represented as a linear combination of the inverse Lomax distribution. Expansions for quantile function, moment generating function, probability weighted moments, ordinary moments, incomplete moments, inverse moments, conditional moments, and Rényi entropy measure are investigated. The new distribution is capable of monotonically increasing, decreasing, reversed J-shaped and upside-down shaped hazard rates. Maximum likelihood estimators of the population parameters are derived. Also, the approximate confi- dence interval of parameters is constructed. A simulation study framework is established to assess the accuracy of estimates through some measures. Simulation outcomes show that there is a great agreement between theoretical and empirical studies. The applicability of the truncated Lomax inverse Lomax model is illustrated through two real lifetime data sets and its goodness-of-fit is compared with that of the recent models. In fact, it provides a better fit to these data than the other competitive models. [ABSTRACT FROM AUTHOR]

In this research article, we propose and study a new model the so-called Marshal-Olkin Kumaraswamy moment exponential distribution. The new distribution contains the moment exponential distribution, exponentiated moment exponential distribution, Marshal Olkin moment exponential distribution and generalized exponentiated moment exponential distribution as special sub-models. Some significant properties are acquired such as expansion for the density function and explicit expressions for the moments, generating function, Bonferroni and Lorenz curves. The probabilistic definition of entropy as a measure of uncertainty called Shannon entropy is computed. Some of the numerical values of entropy for different parameters are given. The method of maximum likelihood is adopted for estimating the model parameters. We study the behavior of the maximum likelihood estimates for the model parameters using simulation study. A numerical study is performed to evaluate the behavior of the estimates with respect to their absolute biases, standard errors and mean square errors for different sample sizes and for different parameter values. Further, we conclude that the maximum likelihood estimates of the Marshal-Olkin Kumaraswamy moment exponential distribution perform well as the sample size increases. We take advantage of applied studies and offer two applications to real data sets that prove empirically the power of adjustment of the new model when compared to other lifetime distributions. [ABSTRACT FROM AUTHOR]

Maximum likelihood estimation (MLE) is often used to estimate the parameters of the circular logistic regression model due to its efficiency under a parametric model. However, evidence has shown that the classical MLE extremely affects the parameter estimation in the presence of outliers. This article discusses the effect of outliers on circular logistic regression and extends four robust estimators, namely, Mallows, Schweppe, Bianco and Yohai estimator BY , and weighted BY estimators, to the circular logistic regression model. These estimators have been successfully used in linear logistic regression models for the same purpose. The four proposed robust estimators are compared with the classical MLE through simulation studies. They demonstrate satisfactory finite sample performance in the presence of misclassified errors and leverage points. Meteorological and ecological datasets are analyzed for illustration. [ABSTRACT FROM AUTHOR]

Modern reliability engineering accelerated life tests (ALT) and partially accelerated life tests (PALT) are widely used to obtain the timely information on the reliability of objects, products, elements, and materials as well as to save time and cost. The ALTs or PALTs are useful in determining the failed manners of the items at routine conditions by using the information of the data generated from the experiment. PALT is the most sensible method to be used for estimating both ordinary and ALTs. In this research, constant stress PALT design for the Fréchet distribution with type-I censoring has been investigated due to a wide applicability of the Fréchet distribution in engineering problems especially in hydrology. The distribution parameters and acceleration factor are obtained by using the maximum likelihood method. Fisher's information matrix is used to develop the asymptotic confidence interval estimates of the model parameters. A simulation study is conducted to illustrate the statistical properties of the parameters and the confidence intervals by using the R software. The results indicated that the constant stress PALT plan works well. Moreover, a numerical example is given to exemplify the performance of the proposed methods. [ABSTRACT FROM AUTHOR]