Abstract
In this paper, we propose a new three-parameter lifetime distribution for modeling symmetric real-life data sets. A simple-type Copula-based construction is presented to derive many bivariate- and multivariate-type distributions. The failure rate function of the new model can be “monotonically asymmetric increasing”, “increasing-constant”, “monotonically asymmetric decreasing” and “upside-down-constant” shaped. We investigate some of mathematical symmetric/asymmetric properties such as the ordinary moments, moment generating function, conditional moment, residual life and reversed residual functions. Bonferroni and Lorenz curves and mean deviations are discussed. The maximum likelihood method is used to estimate the model parameters. Finally, we illustrate the importance of the new model by the study of real data applications to show the flexibility and potentiality of the new model. The kernel density estimation and box plots are used for exploring the symmetry of the used data.
Highlights
The monotonicity asymmetric failure rate function (HRF) of a certain lifetime probabilistic distribution has an important role in modeling real lifetime data
The paper [3] introduced a new two-parameter lifetime model with monotonicity increasing” failure rate (MIFR) named the binomial-exponential-2 (BE2) model, which is constructed as a model of a random sum (RSm) of independent exponential random variables (RVs) when the sample size has a “zero truncated binomial”
The BE2 distribution can be used as an alternative to the Weibull (W), gamma (Gam), exponentiated exponential (EE), and weighted exponential (WhE) distributions in real life applications
Summary
The monotonicity asymmetric failure (hazard) rate function (HRF) of a certain lifetime probabilistic distribution has an important role in modeling real lifetime data. Distributions with the “monotonicity increasing” failure rate (MIFR) function have useful real applications in “pricing”. The survival function (SF) of the binomial exponential-2 (BE2) distribution is given by. Where α > 0 is a scale parameter, GBE2 ( y) = 1 − GBE2 ( y) is the cumulative distribution function (CDF). In the last few decades, many new G families of continuous distributions have been developed. According to [4], the CDF of the TIIHL-G family of distributions is given by. For each baseline GΨ ( y), we can generate a new TIIHL model using (4). Equations (4) and (5) are used for generating the new model
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