In this paper, we first study a new two parameter lifetime distribution. This distribution includes “monotone” and “non-monotone” hazard rate functions which are useful in lifetime data analysis and reliability. Some of its mathematical properties including explicit expressions for the ordinary and incomplete moments, generating function, Renyi entropy, δ-entropy, order statistics and probability weighted moments are derived. Non-Bayesian estimation methods such as the maximum likelihood, Cramer-Von-Mises, percentile estimation, and L-moments are used for estimating the model parameters. The importance and flexibility of the new distribution are illustrated by means of two applications to real data sets. Using the approach of the Bagdonavicius–Nikulin goodness-of-fit test for the right censored validation, we then propose and apply a modified chi-square goodness-of-fit test for the Burr X Weibull model. The modified goodness-of-fit statistics test is applied for the right censored real data set. Based on the censored maximum likelihood estimators on initial data, the modified goodness-of-fit test recovers the loss in information while the grouped data follows the chi-square distribution. The elements of the modified criteria tests are derived. A real data application is for validation under the uncensored scheme.
This paper introduces a new family of continuous distributions called the transmuted transmuted-G family which extends the quadratic rank transmutation map pioneered by Shaw and Buckley [W. T. Shaw, I. R. Buckley, arXiv preprint, 2007 (2007), 28 pages]. We provide two special models of the new family which can be used effectively to model survival data since they accommodate increasing, decreasing, unimodal, bathtub-shaped and increasing-decreasing-increasing hazard functions. We also provide two new characterization theorems of the proposed family. The estimation of the model parameters is performed by the maximum likelihood method. The flexibility of the proposed family is illustrated by means of two applications to real data.
A new five-parameter model called the exponentiated Marshall-Olkin Fréchet distribution is studied. Various of its mathematical properties including ordinary and incomplete moments, quantile and generating functions and order statistics are investigated. The proposed density function can be expressed as a linear mixture of Fréchet densities. The maximum likelihood method is used to estimate the model parameters. The flexibility of the new distribution is proved empirically using two real data sets.
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