Abstract
We introduce a new continuous model with strong physical motivations and wide applications upon compounding the diecreate zero truncated Poisson model and a new continuous model called the Burr X Pareto type II distribution. Some of its mathematical and statistical properties are derived as well as four applications to real data sets are provided with detailes to illustrate the wide importance of the new model. We conclude that the new model is better than other nine competitive models via the four applications. Method of maximum likelihood is used to estimate the unknown parameters of the new model. The new model provide adequate Öts as compared to other related models in the four applications.
Highlights
Introduction and physical motivationA random variable X is said to have the one parameter Pareto type II (PaII) model if its probability density function (PDF) given by gP(βaI)I(x) = (1+xβ)1+β, (1)and cumulative distribution function (CDF)GP(aβI)I (x) = 1 − (1+1x)β, (2)where β is a shape parameter
We introduce a new continuous model with strong physical motivations and wide applications upon compounding the discrete zero truncated Poisson model and a new continuous model called the Burr X Pareto type II distribution
Some of its mathematical and statistical properties are derived as well as four applications to real data sets are provided with details to illustrate the wide importance of the new model
Summary
A random variable (rv) X is said to have the one parameter Pareto type II (PaII) model if its probability density function (PDF) given by gP(βaI)I(x) = (1+xβ)1+β,. GB(αX,IβI)(x) = αβxα−1(1 + xα)−β−1 Due to Yousof et al (2017a), we derive a new model called the Burr X PaII (BXPaII). Model defined by the CDF given by HB(θX,Pβa)II(x) = (1 − exp {−[(1 + x)β − 1]2})θ,. Suppose that we have a system has N subsystems functioning independently at a given time where N has zero truncated Poisson (ZTP) distribution with parameter λ. The probability mass function (PMF) of N is given by pZ(λT)P(N = n)|(n=1,2,...) = [exp( − λ)λn]/{n! Suppose that the failure time of each subsystem has the BXPaII. Some plots of the PDF and HRF for the new PBXPaII model. The PBXPaII density can be right-skewed or unimodal whereas the HRF of the PBXPaII model can be unimodal or unimodal bathtub or bathtub or increasing or unimodal increasing (see Figure 1)
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