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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]

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, 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, 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]