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In this paper, a new two-parameter discrete logistic exponential distribution is proposed based on the survival discretization approach. Some statistical properties are derived, and it is found that the proposed model can be used to discuss several kinds of failure rates including unimodal, bathtub, and increasing-shaped. Moreover, it can be utilized effectively to model under- and over-dispersed data. The distribution parameters are estimated using the maximum likelihood technique. The behavior of maximum likelihood estimators is assessed utilizing a comprehensive simulation study. In the end, two real data are analyzed to show the usefulness of the new discrete distribution. [ABSTRACT FROM AUTHOR]

This paper deals with the statistical inference of the unknown parameters of three-parameter exponentiated power Lindley distribution under adaptive progressive type-II censored samples. The maximum likelihood estimator (MLE) cannot be expressed explicitly, hence approximate MLEs are conducted using the Newton–Raphson method. Bayesian estimation is studied and the Markov Chain Monte Carlo method is used for computing the Bayes estimation. For Bayesian estimation, we consider two loss functions, namely: squared error and linear exponential (LINEX) loss functions, furthermore, we perform asymptotic confidence intervals and the credible intervals for the unknown parameters. A comparison between Bayes estimation and the MLE is observed using simulation analysis and we perform an optimally criterion for some suggested censoring schemes by minimizing bias and mean square error for the point estimation of the parameters. Finally, a real data example is used for the illustration of the goodness of fit for this model. [ABSTRACT FROM AUTHOR]

In the statistical literature, several discrete distributions have been developed so far. However, in this progressive technological era, the data generated from different fields is getting complicated day by day, making it difficult to analyze this real data through the various discrete distributions available in the existing literature. In this context, we have proposed a new flexible family of discrete models named discrete odd Weibull-G (DOW-G) family. Its several impressive distributional characteristics are derived. A key feature of the proposed family is its failure rate function that can take a variety of shapes for distinct values of the unknown parameters, like decreasing, increasing, constant, J-, and bathtub-shaped. Furthermore, the presented family not only adequately captures the skewed and symmetric data sets, but it can also provide a better fit to equi-, over-, under-dispersed data. After producing the general class, two particular distributions of the DOW-G family are extensively studied. The parameters estimation of the proposed family, are explored by the method of maximum likelihood and Bayesian approach. A compact Monte Carlo simulation study is performed to assess the behavior of the estimation methods. Finally, we have explained the usefulness of the proposed family by using two different real data sets. [ABSTRACT FROM AUTHOR]

In the literature of distribution theory, a vast proportion is acquired by discrete distributions and their applications in real-world phenomena. However, in a rapidly changing technological era, the data generated is becoming increasingly complex day by day, making it difficult for us to capture various aspects of this real data through existing discrete models. In view of this, we propose a new flexible discrete distribution with one parameter. Some statistical and reliability are derived. These properties can be expressed as closed-forms. One of the important virtues of this newly evolved model is that it can model not only over-dispersed, positively skewed and leptokurtic data sets, but it can also be utilized for modeling increasing, decreasing and unimodal failure rate. Various estimation approaches are utilized to estimate the model parameter. A simulation study is carried out to examine the performance of the estimators for different sample size. The flexibility of the new model for analyzing different types of data is explained by utilizing four real data sets in different fields. Finally, the proposed model can serve as an alternative model to other distributions in the existing literature for modeling positive real data in several areas. [ABSTRACT FROM AUTHOR]

Linear and circular consecutive models play a vital role to study the mechanical systems emerging in various fields including survival analysis, reliability theory, biological disciplines, and other lifetime sciences. As a result, analysis of reliability properties of consecutive k - out - of - n: F systems has gained a lot of attention in recent years from a theoretical and practical point of view. In the present article, we have studied some important stochastic and aging properties of residual lifetime of consecutive k - out - of - n: F systems under the condition n - k + 1; k ≥ n and all components of the system are working at time t. The mean residual lifetime (MRL) and its hazard rate function are proposed for the linear consecutive k - out - of - n: F (lin/con/k/n:F) and circular consecutive k - out - of - n: F (cir/con/k/n:F) systems. Furthermore, several mathematical properties of the proposed MRL are examined. Finally, the Weibull distribution with two parameters is used as an example to explain the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, a new probability discrete distribution for analyzing over-dispersed count data encountered in biological sciences was proposed. The new discrete distribution, with one parameter, has a log-concave probability mass function and an increasing hazard rate function, for all choices of its parameter. Several properties of the proposed distribution including the mode, moments and index of dispersion, mean residual life, mean past life, order statistics and Lmoment statistics have been established. Two actuarial or risk measures were derived. The numerical computations for these measures are conducted for several parametric values of the model parameter. The parameter of the introduced distribution is estimated using eight frequentist estimation methods. Detailed Monte Carlo simulations are conducted to explore the performance of the studied estimators. The performance of the proposed distribution has been examined by three over-dispersed real data sets from biological sciences. [ABSTRACT FROM AUTHOR]

In this paper, a new flexible generator of distributions is proposed. Some of its fundamental properties including quantile, skewness, kurtosis, hazard rate function, moments, mean deviations, mean time to failure, mean time between failure, availability and reliability function of consecutive linear and circular systems are studied. The hazard rate function can be increasing, decreasing, unimodal-bathtub, unimodal, bathtub, J and inverse J-shaped depending on its parameters values. After introducing the general class, two special models of the new family are discussed in detail. Maximum likelihood and Bayesian methods are used to estimate the model parameters. A detailed simulation study is carried out to examine the bias and mean square error of maximum likelihood and Bayesian estimators. We also illustrate the importance of the new family by means of two distinctive real data sets. It can serve as an alternative model to other lifetime distributions in the existing statistical literature for modeling positive and negative real data in many areas. [ABSTRACT FROM AUTHOR]

Lifetime distributions are an important statistical tools to model the different characteristics of lifetime data sets. The statistical literature contains very sophisticated distributions to analyze these kind of data sets. However, these distributions have many parameters which cause a problem in estimation step. To open a new opportunity in modeling these kind of data sets, we propose a new extension of half-logistic distribution by using the odd Lindley-G family of distributions. The proposed distribution has only one parameter and simple mathematical forms. The statistical properties of the proposed distributions, including complete and incomplete moments, quantile function and Rényi entropy, are studied in detail. The unknown model parameter is estimated by using the different estimation methods, namely, maximum likelihood, least square, weighted least square and Cramer-von Mises. The extensive simulation study is given to compare the finite sample performance of parameter estimation methods based on the complete and progressive Type-II censored samples. Additionally, a new log-location-scale regression model is introduced based on a new distribution. The residual analysis of a new regression model is given comprehensively. To convince the readers in favour of the proposed distribution, three real data sets are analyzed and compared with competitive models. Empirical findings show that the proposed one-parameter lifetime distribution produces better results than the other extensions of half-logistic distribution. [ABSTRACT FROM AUTHOR]

A new distribution defined on (0,1) interval is introduced. Its probability density and cumulative distribution functions have simple forms. Thanks to its simple forms, the moments, incomplete moments and quantile function of the proposed distribution are derived and obtained in explicit forms. Four parameter estimation methods are used to estimate the unknown parameter of the distribution. Besides, simulation study is implemented to compare the efficiencies of these parameter estimation methods. More importantly, owing to the proposed distribution, we provide an alternative regression model for the bounded response variable. The proposed regression model is compared with the beta and unit-Lindley regression models based on two real data sets. [ABSTRACT FROM AUTHOR]

This paper describes a method for computing estimates for the location parameter μ > 0 and scale parameter λ > 0 with fixed shape parameter α of the alpha power exponential distribution (APED) under type-II hybrid censored (T-IIHC) samples. We compute the maximum likelihood estimations (MLEs) of (μ, λ) by applying the Newton-Raphson method (NRM) and expectation maximization algorithm (EMA). In addition, the estimate hazard functions and reliability are evaluated by applying the invariance property of MLEs. We calculate the Fisher information matrix (FIM) by applying the missing information rule, which is important in finding the asymptotic confidence interval. Finally, the different proposed estimation methods are compared in simulation studies. A simulation example and real data example are analyzed to illustrate our estimation methods. [ABSTRACT FROM AUTHOR]

In this article, an extension of the transmuted-G family is proposed, in the so-called Poison transmuted-G family of distributions. Some of its statistical properties including quantile function, moment generating function, order statistics, probability weighted moment, stress-strength reliability, residual lifetime, reversed residual lifetime, Rényi entropy and mean deviation are derived. A few important special models of the proposed family are listed. Stochastic characterizations of the proposed family based on truncated moments, hazard function and reverse hazard function, are also studied. The family parameters are estimated via the maximum likelihood approach. A simulation study is carried out to examine the bias and mean square error of the maximum likelihood estimators. The advantage of the proposed family in data fitting is illustrated by means of two applications to failure time data sets. [ABSTRACT FROM AUTHOR]

In this paper, the estimation of unknown parameters of Chen distribution is considered under progressive Type-II censoring in the presence of competing failure causes. It is assumed that the latent causes of failures have independent Chen distributions with the common shape parameter, but different scale parameters. From a frequentist perspective, the maximum likelihood estimate of parameters via expectation–maximization (EM) algorithm is obtained. Also, the expected Fisher information matrix based on the missing information principle is computed. By using the obtained expected Fisher information matrix of the MLEs, asymptotic 95% confidence intervals for the parameters are constructed. We also apply the bootstrap methods (Bootstrap-p and Bootstrap-t) to construct confidence intervals. From Bayesian aspect, the Bayes estimates of the unknown parameters are computed by applying the Markov chain Monte Carlo (MCMC) procedure, the average length and coverage rate of credible intervals are also carried out. The Bayes inference is based on the squared error, LINEX, and general entropy loss functions. The performance of point estimators and confidence intervals is evaluated by a simulation study. Finally, a real-life example is considered for illustrative purposes. [ABSTRACT FROM AUTHOR]

This paper introduces a new univariate fl exible generator of distributions called the odd Chen-G family, and some of its statistical properties are derived. Two special models of the proposed generator are provided. The model parameters are estimated using six estimation methods, namely, maximum likelihood estimators, least squares estimators, weighted least squares estimators, maximum product of spacings estimators, Cramér-von Mises estimators and percentile based estimators. Further, simulations are performed to compare their performances for both small and large samples. Finally, two real datasets are used to illustrate the fl exibility of the special models of the proposed family. [ABSTRACT FROM AUTHOR]

In this paper, the bivariate extension of the so called Gompertz-G family was introduced and studied in detail. Marshall and Olkin shock model was used to build the proposed bivariate family. The new family was constructed from three independent Gompertz-H families using a minimisation process. Some of its statistical properties such as joint probability density function, coefficient of median correlation, moments, product moment, covariance, conditional probability density function, joint reliability function, stress-strength reliability and joint reversed (hazard) rate function were derived. After introducing the general class, three special models of the new family were discussed. Maximum likelihood method was used to estimate the family parameters. A simulation study was carried out to examine the bias and mean square error of the maximum likelihood estimators. Finally, the importance of the proposed bivariate family was illustrated by means of real dataset, and it was found that the proposed model provides better fi t than other well-known models in the statistical literature such as bivariate Gompertz, bivariate generalized Gompertz, bivariate Gumbel Gompertz, bivariate Burr X Gompertz and bivariate exponentiated Weibull-Gomperz. [ABSTRACT FROM AUTHOR]

This paper introduces a new two-parameter exponentiated discrete Lindley distribution. A wide range of its structural properties are investigated. This includes the shape of the probability mass function, hazard rate function, moments, skewness, kurtosis, stress–strength reliability, mean residual lifetime, mean past lifetime, order statistics and L-moment statistics. The hazard rate function can be increasing, decreasing, decreasing–increasing–decreasing, increasing–decreasing–increasing, unimodal, bathtub, and J-shaped depending on its parameters values. Two methods are used herein to estimate the model parameters, namely, the maximum likelihood, and the proportion. A detailed simulation study is carried out to examine the bias and mean square error of maximum likelihood and proportion estimators. The flexibility of the proposed model is explained by using four distinctive data sets. It can serve as an alternative model to other lifetime distributions in the existing statistical literature for modeling positive real data in many areas. [ABSTRACT FROM AUTHOR]

The aim of our paper is to introduce a new flexible bivariate generalized family of distributions based on Marshall and Olkin shock model, in the so-called the bivariate odd Weibull-G family. The proposed family is constructed from three independent odd Weibull-G families using a minimization process. Creating a bivariate distribution using shock model technique is nothing new, but here, we used only this technique to propose a flexible bivariate family, which has not been considered in the statistical literature yet. Some of its statistical properties are studied. After introducing the general class, one special model of the new family is discussed in detail. Maximum likelihood and Bayesian approaches are used to estimate the model parameters. Further, percentile bootstrap confidence interval and bootstrap-t confidence interval are estimated for the model parameters. A detailed simulation study is carried out to examine the bias and mean square error of the maximum likelihood and Bayesian estimators. Finally, we illustrate the importance of the proposed bivariate family by means of real data set. [ABSTRACT FROM AUTHOR]

For bounded unit interval, we propose a new Kumaraswamy generalized (G) family of distributions through a new generator which could be an alternate to the Kumaraswamy-G family proposed earlier by Cordeiro and de Castro in 2011. This new generator can also be used to develop alternate G-classes such as beta-G, McDonald-G, Topp-Leone-G, Marshall-Olkin-G, and Transmuted-G for bounded unit interval. Some mathematical properties of this new family are obtained and maximum likelihood method is used for the estimation of G-family parameters. We investigate the properties of one special model called the new Kumaraswamy-Weibull (NKwW) distribution. Parameters of NKwW model are estimated by using maximum likelihood method, and the performance of these estimators are assessed through simulation study. Two real life data sets are analyzed to illustrate the importance and flexibility of the proposed model. In fact, this model outperforms some generalized Weibull models such as the Kumaraswamy-Weibull, McDonald-Weibull, beta-Weibull, exponentiated-generalized Weibull, gamma-Weibull, odd log-logistic-Weibull, Marshall-Olkin-Weibull, transmuted-Weibull and exponentiated-Weibull distributions when applied to these data sets. The bivariate extension of the family is also proposed, and the estimation of parameters is dealt. The usefulness of the bivariate NKwW model is illustrated empirically by means of a real-life data set. [ABSTRACT FROM AUTHOR]

The extreme value theory is expanded by proposing and studying a new version of the Fréchet model. Some new bivariate type extensions using Farlie–Gumbel–Morgenstern copula, modified Farlie–Gumbel–Morgenstern copula, Clayton copula, and Renyi's entropy copula are derived. After a quick study for its properties, different non-Bayesian estimation methods under uncensored schemes are considered, such as the maximum likelihood estimation method, Anderson–Darling estimation method, ordinary least square estimation method, Cramér–von-Mises estimation method, weighted least square estimation method, left-tail Anderson–Darling estimation method, and right-tail Anderson–Darling estimation method. Numerical simulations were performed for comparing the estimation methods using different sample sizes for three different combinations of parameters. The Barzilai–Borwein algorithm was employed via a simulation study. Three applications were presented for measuring the flexibility and the importance of the new model for comparing the competitive distributions under the uncensored scheme. Using the approach of the Bagdonavicius–Nikulin goodness-of-fit test for validation under the right censored data, we propose a modified chi-square goodness-of-fit test for the new model. The modified goodness-of-fit statistic test was applied for the right censored real data set, called leukemia free-survival times for autologous transplants. Based on the maximum likelihood estimators on initial data, the modified goodness-of-fit test recovered the loss in information while the grouping data and followed chi-square distributions. All elements of the modified goodness-of-fit criteria tests are explicitly derived and given. [ABSTRACT FROM AUTHOR]

Alizadeh et al. introduced a flexible family of distributions, in the so-called Gompertz-G family. In this article, a discrete analogue of the Gompertz-G family is proposed. We also study some of its distributional properties and reliability characteristics. After introducing the general class, three special models of the new family are discussed in detail. The maximum likelihood method is used for estimating the family parameters. A simulation study is carried out to assess the performance of the family parameters. Finally, the flexibility of the new family is illustrated by means of four genuine datasets, and it is found that the proposed model provides a better fit than the competitive distributions. [ABSTRACT FROM AUTHOR]

Burr proposed twelve different forms of cumulative distribution functions for modeling data. Among those twelve distribution functions is the Burr X distribution. In statistical literature, a flexible family called the Burr X-G (BX-G) family is introduced. In this paper, we propose a bivariate extension of the BX-G family, in the so-called bivariate Burr X-G (BBX-G) family of distributions based on the Marshall–Olkin shock model. Important statistical properties of the BBX-G family are obtained, and a special sub-model of this bivariate family is presented. The maximum likelihood and Bayesian methods are used for estimating the bivariate family parameters based on complete and Type II censored data. A simulation study was carried out to assess the performance of the family parameters. Finally, two real data sets are analyzed to illustrate the importance and the flexibility of the proposed bivariate distribution, and it is found that the proposed model provides better fit than the competitive bivariate distributions. [ABSTRACT FROM AUTHOR]