Abstract
We propose a five parameter transmuted geometric quadratic hazard rate (TG-QHR) distribution derived from mixture of quadratic hazard rate (QHR), geometric and transmuted distributions via the application of transmuted geometric-G (TG-G) family of Afify et al.(Pak J Statist 32(2), 139-160, 2016). Some of its structural properties are studied. Moments, incomplete moments, inequality measures, residual life functions and some other properties are theoretically taken up. The TG-QHR distribution is characterized via different techniques. Estimates of the parameters for TG-QHR distribution are obtained using maximum likelihood method. The simulation studies are performed on the basis of graphical results to illustrate the performance of maximum likelihood estimates (MLEs) of the TG-QHR distribution. The significance and flexibility of TG-QHR distribution is tested through different measures by application to two real data sets.
Highlights
Generalizations and extensions of the probability distributions are more flexible and suitable for many real data sets as compared to the classical distributions
We perform two simulation studies based on graphical results by using selected transmuted geometric quadratic hazard rate (TG-quadratic hazard rate (QHR)) distributions
We can perceive that TG-QHR model is accurate fitted to data II because good of fit measures are smaller and graphical plots such as estimated pdf, cdf and pp. plots are closer to data set II (Fig. 6)
Summary
Generalizations and extensions of the probability distributions are more flexible and suitable for many real data sets as compared to the classical distributions. Cordeiro et al (2017) studied generalized odd log-logistics family of distributions in terms of various characteristics and applications. The basic motivations for proposing the TG-QHR distribution are: (i) to generate distributions with arc, positively skewed, negatively skewed and symmetrical shaped; (ii) to obtain increasing, decreasing and inverted bathtub hazard rate function; (iii) to serve as the best alternative model for the current models to explore and modeling real data in economics, life testing, reliability, survival analysis manufacturing and other areas of research and (iv) to provide better fits than other sub-models. The pdf and cdf of a random variable X with TG-QHR distribution are obtained by inducting (4) and (5) in (1) and (2) as follows f ðxÞ θ Aðxjα; β; γÞ e−Qðxjα;β;γÞ 1⁄21 þ ðθ−1Þð1−e−Qðxjα;β;γÞÞ2. Residual life functions The residual life, say mn(t), of X with TG-QHR distribution is mnðtÞ 1⁄4 E1⁄2ðX−tÞnjX > t; Zλ mnðtÞ
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