Abstract
We study a new family of distributions defined by the minimum of the Poisson random number of independent identically distributed random variables having a Topp Leone-G distribution (see Rezaei et al., (2016)). Some mathematicalproperties of the new family including ordinary and incomplete moments, quantile and generating functions, mean deviations, order statistics, reliability and entropies are derived. Maximum likelihood estimation of the model parameters is investigated. Some special models of the newfamily are discussed. An application is carried out on real data set applications sets to show the potentiality of the proposed family.
Highlights
The statistical literature contains many new classes of distributions which have been constructed by extending common families of continuous distributions and give more flexibility by adding one or more parameters to the baseline model
Several classes of distributions have been constructed by extending common families of continuous distributions. These generalized distributions give more flexibility by adding one "or more" parameters to the baseline model. They were pioneered by Gupta et al (1998) who proposed the exponentiated-G class, which consists of raising the cumulative distribution function (CDF) to a positive power parameter
The mean inactivity time (MIT) or mean waiting time (MWT) called the mean reversed residual life function is given by M1(t) = E[(t − X)| X ≤ t], and it represents the waiting time elapsed since the failure of an item on condition that this failure had occurred in (0, t) .The MIT of the Poisson Topp Leone-G (PTL-G) family of distributions can be obtained by setting n = 1 in the above equation
Summary
The statistical literature contains many new classes of distributions which have been constructed by extending common families of continuous distributions and give more flexibility by adding one or more parameters to the baseline model. Several classes of distributions have been constructed by extending common families of continuous distributions These generalized distributions give more flexibility by adding one "or more" parameters to the baseline model. They were pioneered by Gupta et al (1998) who proposed the exponentiated-G class, which consists of raising the cumulative distribution function (CDF) to a positive power parameter.
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