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The competing risks model plays an important role in the statistical analysis of engineering, econometric, biological and other fields. A tested product may fail from different causes. Therefore, these failure causes as if competing with each other to bring about the failure of tested products (an experimental unit). Hence, in the statistical literature, this is known as the competing risk problem and it has been studied quite extensively by several researchers when the lifetime of the product is the latent failure time of the first failure cause among all the possible failure causes. In this paper, a competing risks model based on a generalized progressive hybrid type-I (GPH type-I) censoring is considered when the latent lifetime distributions of failure causes are inverse Weibull (IW) distributed and partially observed. We established various estimation methods including Maximum likelihood estimates (MLEs) and Bayes estimates (BEs). MLEs with the corresponding asymptotic confidence intervals are obtained. Bayes estimates of the parameters are obtained based on squared error loss (SEL) function under the assumption of independent gamma priors. Furthermore, we applied Markov Chain Monte Carlo (MCMC) techniques to compute BEs and to calculate the credible intervals. Finally, simulation studies and real data set are used for illustrative purpose. [ABSTRACT FROM AUTHOR]

In this paper, we propose a flexible family called the exponentiated alpha-power-G (EAP-G) family. The benefits of the proposed family include its analytical simplicity and its ability to confer flexibility to the baseline distributions in survival analysis. Based on the proposed approach, a three-parameter extension of the exponential distribution called the exponentiated alpha-power exponential (EAPE) distribution is studied in detail. Maximum likelihood is used to estimate the EAPE parameters, and its performance is evaluated via a simulation study. Furthermore, two real-world survival data are used to demonstrate the applicability and examine the flexibility of the proposed distribution. The EAPE distribution is compared to other competing generalizations of the exponential distribution. The real data analysis shows that the proposed model performed better among the competitors and could potentially be very adequate in describing and modeling a wide range of survival data. [ABSTRACT FROM AUTHOR]

There are many situations in reliability or medical studies, where items may fail due to one of several causes. Further, censoring is unavoidable in any life testing. In this paper attempts to estimate problem for the competing risks model where the data are adaptive type-II progressive hybrid censored scheme and follow the inverse Weibull distribution. In this regards, we obtain the maximum likelihood estimation of the parameters and the asymptotic confidence intervals for the unknown parameters. Further, Bayes estimates of the parameters which obtained based on squared error and LINEX loss functions under the assumptions of independent gamma priors. For Bayesian estimation, we take advantage of Markov Chain Monte Carlo techniques by applying the Metropolis-Hasting algorithm under the square error and LINEX loss function to derive Bayesian estimators. Finally, two data sets with a Monte Carlo simulation study and a real data set of the electronic applications are analyzed for illustrative purposes. [ABSTRACT FROM AUTHOR]

This paper presents, a new family of distributions, named the generalized linear failure rate family, generated from a generalized linear failure rate random variable is introduced. The new family contains five well-known families as special cases. Four particular distributions stemmed from the new family are explored. Mathematical properties of interest of the new family are derived. The maximum likelihood method is used to estimate the model parameters and its behavior is explored via detailed simulations. Finally, the importance of the new family is illustrated through two applications extracted from practice. [ABSTRACT FROM AUTHOR]

Bayes estimation methods are proposed in this paper to estimate the unknown parameters of the Alpha Power Inverted Exponential (APIE) distribution for complete sample and this distribution was introduced by Unal, Cakmakyapan and Ozel (2018). Lindley's approximation, Tierney and Kadane's (T-K) approximation and Markov Chain Monte Carlo (MCMC) method are used for obtaining bayes estimators with squared error loss function (SELF) and Gamma prior for the unknown parameters of this distribution. The performance of these estimators are compared with maximum likelihood estimators by simulation study and the comparison is based on MSE's. Also two real life data sets are used to illustrate the usefulness of the Alpha Power Inverted Exponential (APIE) distribution. Different criterions are used to access the goodness of fit of APIE distribution as compared to other distributions. [ABSTRACT FROM AUTHOR]

The family of distributions which are derived from baseline distributions drag the attention of researchers from past recent years. In this paper we introduce an extension of Gumbel type-II by using transmutation approach suggested by Shaw and Buckley (2007). Several distributional properties of the explored distribution, such as moments, moment generating function, quantile function, reliability analysis, order statistics, and Renyi entropy, have been discussed. Various diagrams depict the behaviour of the probability density function (pdf) and cumulative distribution function (cdf). The parameters of the explored distribution are calculated by using the well-known maximum likelihood procedure. Eventually, the utility of the explored distribution is shown using real life data sets. [ABSTRACT FROM AUTHOR]

In this paper, for the first time, the impact of identification problem on probability distribution parameters is studied, effects of the identification problem are investigated in a new empirical distribution naming the inverted power Topp-Leone (IPTL) distribution, some mathematical properties are derived for the identified distribution. A simulation study is performed to study the behavior of identified estimators using the maximum likelihood method (MLE) and to illustrate the impact of ignoring the identification problem, a real data set is applied to investigate the identified distribution flexibility and a practical comparison between the identified and the non-identified IPTL distribution is performed. [ABSTRACT FROM AUTHOR]

In this paper, a new generalized family of distributions called the exponentiated odd Weibull-Topp-Leone-G (EOW-TL-G) family of distributions is presented. A linear representation of the proposed model is also presented. A simulation study to examine the consistency of the maximum likelihood estimates is conducted. Usefulness of the new proposed model was assessed by means of applications to two real data examples. [ABSTRACT FROM AUTHOR]

In this paper, we attempt to supplement the distribution theory literature by incorporating a new bounded distribution, called the bounded exponentiated Weibull (BEW) distribution in the (0,1) intervals by transformation method. The proposed distribution exhibits decreasing, increasing, bathtub and right-skewed unimodal density while the hazard rate can have decreasing and bathtub shaped. Although our main focus is on the construction of chi-squared goodness-of-fit tests for the BEW distribution for right censored data based on Nikulin-Rao-Robson (NRR) statistic and its modification, in addition, we derive some basic statistical properties of the proposed BEW distribution. The test statistic used is the modified chi-squared statistic Y², developed by Bagdonavicius and Nikulin (2011) for some parametric models when data are censored. The performances of the proposed test is investigated through an extensive simulation study. An application to a real data set is also provided. The main purpose of this work is the construction of chisquared goodness of-fit tests for the transmuted generalized linear exponential distribution with unknown parameters and right censoring. The criterion test used is the modified chisquared statistic Y², developed by Bagdonavicius and Nikulin (2011) for some parametric models when data are censored. The performances of the proposed test is investigated through an extensive simulation study. An application to a real data set is also provided. [ABSTRACT FROM AUTHOR]

In this paper, we proposed a new model, capable of modeling against the bathtub shaped failure rate phenomena, referred to as the Lehmann-II Muhammad (L-II-M) distribution. We derived some mathematical and reliability characteristics developed some explicit expressions for the moments, quantile function, and order statistics. We suggested a method of maximum likelihood estimator for the estimation of model parameters, and a simulation study was recommended to observe the asymptotic behavior of MLEs. The strength of L-II-M distribution was affirmed by modeling in two suitable lifetime engineering datasets. [ABSTRACT FROM AUTHOR]

This research paper deals with formulation of Poisson-Pranav probability distribution by combining Poisson distribution and Pranav distribution for count data. Some important structural and statistical properties of this model are derived and discussed like coefficient of variation, skewness, kurtosis, reliability analysis and order statistics are beening obtained. Also for obtaining estimate of unknown parameter of this distribution maximum likelihood estimation method is used. At last we fitted our proposed model to real life data set to check its suitability and applicability compared to other related models. [ABSTRACT FROM AUTHOR]

In this paper, we have presented a discrete version of Modified Inverse Rayleigh Distribution. We proposed Discrete Modified Inverse Rayleigh distribution. We have derived the reliability properties including survival function, residual reliability function hazard rate function, second rate of failure along with their graphical portray. Further distributional properties like quantile function, skewness, kurtosis, mean deviation and the distribution of order statistics of the proposed distribution are also presented. The estimation of parameters has been done by method of proportion, maximum likelihood method and method of moments. A simulation study has been conducted by these methods for different sample sizes. The suitability is shown by applying the new model on the real data sets. Goodness of the new model on over-dispersed data set is also shown. [ABSTRACT FROM AUTHOR]

In this paper, we introduce Exponentiated generalized inverse Rayleigh distribution and study its different structural properties. The parameters of the proposed distribution have been estimated through the method of maximum likelihood estimation. Further, two types of data sets are considered for making the comparison among special cases of EGIR distribution in terms of model fitting. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new class of lifetime distributions called the Marshall- Olkin Generalized G Poisson family. The proposed family of distributions is constructed by compounding the Marshall-Olkin Generalized distribution with the truncated Poisson distribution. It can provide better fits than some of the known lifetime distributions and this fact represents a good characterization of this new family. Some useful characterizations for the new family are presented. The maximum likelihood method is used for estimating the model parameters. The importance and flexibility of the new family are illustrated by means of an application to a real data set. [ABSTRACT FROM AUTHOR]

In this paper a product generalized Pearson (PGP) type VII distribution is proposed by taking the product of two generalized Pearson type VII probability densities functions (pdfs). Some properties of PGP type VII distribution are investigated including its pdf, cumulative distribution function (cdf), moments, hazard rate function, cumulative hazard rate function, survival function, mean residual function and their graphs, maximum likelihood estimators and their asymptotic variances and mixed random variables are derived. The characterization of PGP type VII distribution is presented through conditional expectation. A simulation study is used to find the estimates of parameters of PGP type VII distribution. Finally, an application of PGP type VII distribution to a real data set is shown. [ABSTRACT FROM AUTHOR]

This paper discusses maximum likelihood and Bayes estimation of the two unknown parameters of Nadarajah and Haghighi distribution based on record values. It assumed that in Bayes case, the unknown parameters of Nadarajah and Haghighi distribution have gamma prior densities. Explicit forms of Bayes estimators cannot be obtained. Lindley approximation is exploited to obtain point estimators for the unknown parameters. The Bayesian and non-Bayesian predictions of both point and interval predictions of the future record values are also discussed. A simulation study is used to the comparison between the Bayesian and non-Bayesian methods. Analysis of a real dataset is presented for illustrative purposes. [ABSTRACT FROM AUTHOR]

In this paper inverted Kumaraswamy distribution is introduced. Some of its properties are presented through, some models of stress strength, measures of central tendency and dispersion and order statistics. Some sub-models, limiting distributions and the relation between inverted Kumaraswamy and other distributions are derived. The maximum likelihood and Bayes estimators, confidence intervals for the parameters, the reliability and the hazard rate functions of the inverted Kumaraswamy distribution based on Type II censored samples are obtained. A numerical study is carried out to illustrate the theoretical results for both approaches, the maximum likelihood and the Bayesian estimation. Moreover, the results are applied on real data. [ABSTRACT FROM AUTHOR]

The skew-generalized inverse weibull distribution (SGIW) has four parameters of lifetime distribution. It could have different hazard rates: increasing, decreasing and unimodal. In this paper, the method of Azzalini's (1985) is used to provide a shape of parameter to generalize inverse weibull, which creates a new class of skew-generalized inverse weibull distributions. Different statistical properties of this new distribution are discussed whereas expressions for density, minimum and maximum order statistic and ith moment of the order statistics and the inference of the old parameters and the skewness parameter are studied. In addition, Mont Carlo simulation method was carried out to investigate the properties of the estimations of the unknown parameters of SGIW. Furthermore, the flexibility of SGIW model is illustrated by means of two real data sets applications. [ABSTRACT FROM AUTHOR]

In this paper, a new two-parameter discrete distribution is introduced which is in fact an analogue of the continuous generalized Rayleigh distribution, called discrete generalized Rayleigh distribution. The one parameter discrete Rayleigh distribution is obtained as a particular case. Several important distributional and reliability properties such as survival and hazard rate functions, moments, order statistics, unimodality and infinite divisibility of the proposed distribution are examined. A related characterization of the distribution is also provided. Parameter estimation, using different methods, namely methods of moments, maximum likelihood and proportion, is discussed. Performance of the different estimation methods are compared by means of a Monte Carlo simulation. Finally, two real data sets are analyzed to investigate the suitability of the proposed distribution in modeling count data. [ABSTRACT FROM AUTHOR]

In this paper, we have introduced a new generalization of the Exponentiated Pareto-I distribution named as the Transmuted Exponentiated Pareto-I distribution. The new distribution can model data with increasing, decreasing or constant hazard rate. The suitability of the distribution in modeling breaking strength of materials is highlighted with real data sets. Furthermore, we have derived some properties of the distribution including characteristic function, mean deviations, information entropies and order statistics of the new distribution. The estimation of distribution parameters has been done using Maximum Likelihood method. Finally, we have provided application of the new proposed distribution using two real data sets. It has been observed that the new distribution works better than the Pareto-I, Exponentiated Pareto-I and the Transmuted Pareto-I distributions for both data sets. [ABSTRACT FROM AUTHOR]

In this paper, a five parameter Lindley Distribution (FPLD) is proposed as a new generalization of the basic Lindley distribution. The structural properties of the new distribution are investigated. These include the compounding representation of the distribution, reliability analysis and statistical measures. Expressions for Lorenz and Bonferroni curves and Renyi entropy as a measure for uncertainty reduction are derived. Maximum likelihood estimation is used to evaluate the parameters. The new model contains twelve lifetime distributions as special cases such as the Lindley, Quasi Lindley, gamma, and exponential distributions, among others. This model has the advantage of being capable of modeling various shapes of aging and failure criteria. Finally, the usefulness of the new model for modeling reliability data is illustrated using a real data set. [ABSTRACT FROM AUTHOR]

In this paper, the stress-strength reliability is obtained when the underlying distribution has power hazard function. Maximum likelihood and uniformly minimum variance unbiased estimate of the stress-strength reliability are derived and various distributional properties of these estimates are discussed. Exact and asymptotic confidence intervals for the stress-strength reliability are constructed. Simulation study is also performed to investigate the coverage probabilities of these intervals. [ABSTRACT FROM AUTHOR]

In this paper, we use the local influence method introduced by Cook (1986) to study for regression diagnostics in the linear model with stochastic linear restrictions. We assume normality and use a likelihood-based approach. We establish the normal curvatures for identifying influencial observations under several schemes. [ABSTRACT FROM AUTHOR]

This paper presents a review about the theory of regression analysis based on Jørgensen's dispersion models, which extends the classical theory of generalized linear models (GLMs). Dispersion models provide a rich class of parametric models useful to conduct regression analysis of non-normal data, which contain all the error distributions considered in the classical GLMs. One example used to illustrate the extension is the simplex GLM for continuous proportional data. Details concerning the maximum likelihood estimation are presented, accompanied with some numerical results. [ABSTRACT FROM AUTHOR]