In this paper, we introduce an extension of the inverse Lindley distribution, which offers more flexibility in modeling upside-down bathtub lifetime data. Some statistical properties of the proposed distribution are explicitly derived. These include density and hazard rate functions with their behavior, moments, moment generating function, skewness, kurtosis measures, and quantile function. Maximum likelihood estimation of the parameters and their estimated asymptotic distribution and confidence intervals are derived. Rényi entropy as a measure of the uncertainty in the model is derived. The application of the model to a real data set i.e., the flood levels for the Susquehanna river at Harrisburg, Pennsylvania, over 20 four-year periods from 1890 to 1969 is compared to the fit attained by some other well-known existing distributions.

No abstract

No abstract

This paper proposes the new three-parameter type I half-logistic inverse Weibull (TIHLIW) distribution which generalizes the inverse Weibull model. The density function of the TIHLIW can be expressed as a linear combination of the inverse Weibull densities. Some mathematical quantities of the proposed TIHLIW model are derived. Four estimation methods, namely, the maximum likelihood, least squares, weighted least squares, and Cramér–von Mises methods, are utilized to estimate the TIHLIW parameters. Simulation results are presented to assess the performance of the proposed estimation methods. The importance of the TIHLIW model is studied via a real data application.

In this study a new lifetime class with decreasing failure rate is introduced by compounding truncated logarithmic distribution with any proper continuous lifetime distribution. The properties of the proposed class are discussed, including a formal proof of itsprobability density function, distribution function and explicit algebraic formulae for its reliability and failure rate functions. A simple EM-type algorithm for iteratively computing maximum likelihood estimates is presented. A formal equation for Fisher information matrix is derived in order to obtaining the asymptotic covariance matrix. Thisnew class of distributions generalizes several distributions which have been introduced and studied in the literature."

In this paper, we introduce a new generalization of a class of inverse Lindley distributions called the generalized inverse Lindley power series (GILPS) distribution. This class of distributions is obtained by compounding the generalized class of inverse Lindley distributions with the power series family of distributions. The GILPS contains several lifetime subclasses such as inverse Lindley power series, two parameters inverse Lindley power series, and inverse power Lindley power series distributions. It can generate many statistical distributions such as the inverse power Lindley Poisson distribution, the inverse power Lindley geometric distribution, the inverse power Lindley logarithmic distribution, and the inverse power Lindley binomial distribution. The proposed class has flexibility in the sense that it can generate new lifetime distributions as well as some existing distributions. For the proposed class, several properties are derived such as hazard rate function, limiting behavior, quantile function, moments, moments generating function, and distributions of order statistics. The method of maximum likelihood estimation can be used to estimate the model parameters of this new class. A simulation for a selective model will be discussed. At the end, we will demonstrate applications of three real data sets to show the flexibility and potential of the new class of distributions.

In this study, we introduce a new familyof models for lifetime data called generalized extended Weibullpower series family of distributions by compoundinggeneralizedextended Weibull distributions and power series distributions. The compounding procedure follows the same setup carried out by Adamidis (1998). The proposed family contains all types of combinations between truncated discrete with generalized and nongeneralized Weibull distributions. Some existing power series and subclasses of mixed lifetime distributions become special cases of the proposed family, such as the compound class of extended Weibull power seriesdistributions proposed by Silva et al. (2013) and the generalized exponential power series distributionsintroduced by Mahmoudi and Jafari (2012).Some mathematical properties of the new class are studied, includingthe cumulative distribution function, density function, survival function, and hazard rate function. The method of maximum likelihood is used for obtaining a general setup for estimating the parameters of any distribution in this class. An expectation-maximization algorithm is introduced for estimating maximum likelihood estimates.Special subclasses and applications for some models in areal datasetare introduced to demonstrate the flexibility and the benefit of this new family.

In this study, we introduce a new family of models for lifetime data called generalized extended Weibull power series family of distributions by compounding generalized extended Weibull distributions and power series distributions. The compounding procedure follows the same setup carried out by Adamidis (1998). The proposed family contains all types of combinations between truncated discrete with generalized and non-generalized Weibull distributions. Some existing power series and subclasses of mixed lifetime distributions become special cases of the proposed family, such as the compound class of extended Weibull power series distributions proposed by Silva et al. (2013) and the generalized exponential power series distributions introduced by Mahmoudi and Jafari (2012). Some mathematical properties of the new class are studied, including the cumulative distribution function, density function, survival function, and hazard rate function. The method of maximum likelihood is used for obtaining a general setup for estimating the parameters of any distribution in this class. An expectation-maximization algorithm is introduced for estimating maximum likelihood estimates. Special subclasses and applications for some models in a real dataset are introduced to demonstrate the flexibility and the benefit of this new family.