Abstract
In this paper, we introduced a new three-parameter probability model called Poisson generalized half logistic (PoiGHL). The new model possesses an increasing, decreasing, unimodal and bathtub failure rates depending on the parameters. The relationship of PoiGHL with the exponentiated Weibull Poisson (EWP), Poisson exponentiated Erlang-truncated exponential (PEETE), and Poisson generalized Gompertz (PGG) model is discussed. We also characterized the PoiGHL sub model, i.e the half logistic Poisson (HLP), based on certain functions of a random variable by truncated moments. Several mathematical and statistical properties of the PoiGHL are investigated such as moments, mean deviations, Bonferroni and Lorenz curves, order statistics, Shannon and Renyi entropy, Kullback-Leibler divergence, moments of residual life, and probability weighted moments. Estimation of the model parameters was achieved by maximum likelihood technique and assessed by simulation studies. The stress-strength analysis was discussed in detail based on maximum likelihood estimation (MLE), we derived the asymptotic confidence interval of based on the MLEs, and examine by simulation studies. In three applications to real data set PoiGHL provided better fit and outperform some other popular distributions. In the stress-strength parameter estimation PoiGHL model illustrated as a reliable choice in reliability analysis as shown using two real data set.
Highlights
Most of the classical distributions used in the reliability studies are based on some certain assumptions and are not capable in accommodating non-monotone failure rates
1+ e − e a LPoiGHL can be use in the estimation of univariate survival function for censored data via linear location-scale regression modeling defined by yi = μi + σzi, i = 1, · · ·, n, where yi ∼ LPoiGHL model given by (22), μi = xiT β is the location of yi, zi is the random error with density in (23), xi = is a vector of known explanatory random variables associated with yi
The performance of confidence interval based on the maximum likelihood estimation (MLE) is quite good and the ALCI decreases as the sample sizes increases
Summary
Most of the classical distributions used in the reliability studies are based on some certain assumptions and are not capable in accommodating non-monotone failure rates. Several attempts have been made to propose a new parametric model from the existing classical one in the last few decade The advantage of these approaches for constructing a new probability model lies in the flexibility to model both monotonic and non-monotonic failure rate functions even though the existing distribution (or baseline) may have a monotonic failure rate. One of these techniques that receive significant attention is the convolution of the continuous and discrete probability model.
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