Iwueze’s Distribution and Its Application

Abstract

Increased usage of single parameter life-time distributions for reference in development of other life-time distributions and data modeling has attracted the interest of researchers. Because performance ratings differ from one distribution to another and there are increased need for distributions that delivers improved fits, new distributions with a better performance rating capable of providing improved fits have evolved in the Literature. One of such distribution is the Iwueze's distribution. Iwueze's distribution is proposed as a new distribution with Gamma and Exponential baseline distributions. Iwueze's distribution theoretical density, distribution functions and statistical features such as its moments, factors of variation, skewness, kurtorsis, reliability functions, stochastic ordering, absolute deviations from average, absolute deviations from mid-point, Bonferroni and Lorenz curves, Bonferroni and Gini indexes, entropy and the stress and strength reliability have been developed. Iwueze's distribution curve is not bell-shaped, but rather skewed positively and leptokurtic. The risk measurement function is a monotone non-decreasing function, while the average residual measurement life-time function is a monotone non-increasing function. The parameter of the Iwueze's distribution was estimated using the likelihood estimation approach. When used for a real-life data modeling, the new proposed Iwueze's distribution delivers improved and superior fits better than the

On the Statistical Properties of the Remkan Distribution

“…The survivorship or existence measurement function (also known as survival function) is defined as the probability that an item does not fail prior to sometime t (Elechi et al [7], Epstein [8], Ronald et al [10], Shanker and Shukla [16]).…”

“…The risk measurement function (also known as hazard rate function) on the other hand can be seen as the conditional probability of failure given that it has survived to the time t (Elechi et al [7], Ronald et al [10], Shanker [15], Umeh and Ibenegbu [21]).…”

“…These two distributions are known to have their weaknesses. The weakness of the Exponential distribution is that the hazard rate function is constant; hence, it cannot handle datasets with monotone non-decreasing hazard rates (Elechi et al [7], Epstein [8], Ronald et al [10], Shukla [20], Shukla [19]). Furthermore, the weakness of the Gamma distribution is that the survival rate function cannot be expressed in closed form (Elechi et al [7], Shanker [12,13]).…”

“…The weakness of the Exponential distribution is that the hazard rate function is constant; hence, it cannot handle datasets with monotone non-decreasing hazard rates (Elechi et al [7], Epstein [8], Ronald et al [10], Shukla [20], Shukla [19]). Furthermore, the weakness of the Gamma distribution is that the survival rate function cannot be expressed in closed form (Elechi et al [7], Shanker [12,13]). The weaknesses of these two distributions are what the aforementioned one-parameter and two-parameter distributions address, providing distributions whose survival rate function can be expressed in closed form and hazard rate functions capable of handling datasets with monotone non-decreasing hazard rates.…”

The Remkan Distribution and Its Applications

“…Examples of the one-parameter lifetime distributions that has been proposed over the years includes the Exponential distribution [3], Lindley distribution [4], Akash distribution [5], Sujatha distribution [6], Ishita distribution [7], Akshaya distribution [8]. Others include Rama distribution [9], Pranav distribution [10], Odoma distribution [11], Nwikpe distribution [12], Iwueze distribution [13], Juchez distribution [14], Chris-Jerry distribution [15].…”