Abstract
Objectives: Probability distributions have great use in reliability engineering where the researchers try to find the distribution of the different processes. To meet the needs of the reliability engineers, we have proposed a simple probability distribution named as Beta Lehman-2 which may be proved more useful as compared to already existing models of the probability distributions. The aim of the study is to show the performance of the proposed distribution over already existing distributions. Methods: In this study, a new Beta Lehmann-2 Power function distribution (BL2PFD) is proposed. We suggest a new generator that will modify the Power function distribution called Beta Lehmann-2 generator (BL2-G). Findings: The various properties of the new distribution have been discussed in detail such as moments, vitality function, conditional moments and order statistics etc. We have also characterized the BL2PFD based on conditional variance. This distribution can be used for approximately symmetric data (normal data), positive and negative skewed data. Application: The application of this distribution is illustrated by using data sets from medical and engineering sources. The shape of the new distribution has been studied for applied sciences. After analyzing data, we conclude that the proposed model BL2PFD perform better in all the data sets while compared to different competitor models. Keywords: Beta Lehmann-2 Power function distribution; Characterization of truncated distribution; Lehmann alternatives; Percentile estimator; Power function distribution
Highlights
The researchers in Engineering sciences mostly study the reliability of different components by taking the help from probability distributions that are simple in mathematical expression instead of using mathematically complex probability distributions
Let x1, x2, x3, . . . , xn be a random sample of size n drawn from Probability density function of Beta Lehmann-2 Power function distribution (BL2PFD)
The comparison of the Probability distributions has been made in all the data sets on the basis of Akaike information criterion (AIC), the correct Akaike information criterion (CAIC), Bayesian information criterion (BIC) and Hannan-Quinn information criterion (HQIC)
Summary
The researchers in Engineering sciences mostly study the reliability of different components by taking the help from probability distributions that are simple in mathematical expression instead of using mathematically complex probability distributions. In Dallas [1] introduced the power function as the inverse of Pareto distribution. Meniconi and Barry [2] showed that power function distribution is better to fit for failure data. Estimation of the parameters of the two-parameter Power function distribution was studied by Zaka and Akhter[7] through the methods of the least squares, relative least squares and ridge regression. By using the Bayesian inference, Hanif et al[9] estimated the parameter of the one-parameter Power function distribution. In Okorie et al [12] proposed the modification of the Power function distribution by using Marshall and Olkin Marshall and Olkin [13] technique. Further Zaka et al[17] introduced the exponentiated generalized class of power function distribution
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