A Two-Parameter Pranav Distribution with Properties and Its Application.

Abstract

Introduction: Lifetime distribution has drawn so much attention in recent research, and this has lead to the development of new lifetime distribution. Addition of parameters to the existing distribution makes the distribution more flexible and reliable and applicable model has become the focus of the recent search. This paper proposed a two-parameter Pranav distribution which has its base from a one-parameter Pranav and Ishita distribution. Methods Two parameter Pranav distribution was proposed. Mathematical and statistical properties of the distribution which includes; moments, coefficient of variation, skewness, kurtosis, index of dispersion, hazard rate function, mean residual life function, stochastic ordering, mean deviation, Bonferroni and Lorenz curves were developed. Other lifetime distributions such as Ishita, Akash, Sujatha, Shanker, Lindley, and Exponential distributions were considered in the study. Results: This new distribution was compared with two-parameter Akash, Lindley, one parameter Pranav, Ishita, Akash, Sujatha, Shanker, Lindley, and Exponential distributions to determine the efficiency of the new model. The estimation of parameters has been X-rayed using the method of moments and maximum likelihood. Also, AIC and BIC were used to test for the goodness of fit of the model which was applied to a real-life data of hypertensive patients. The results show that the new two-parameter Pranav distribution has the lowest value of AIC and BIC Conclusion: Based on the AIC and BIC values we can conclude that the two-parameter Pranav is more efficient than the other distribution for modeling survival of hypertensive patients. Hence two-parameter Pranav can be seen as an important distribution in modeling lifetime data.

The Remkan Distribution and Its Applications

“…The dataset employed represents the lifetime data relating to time (in months from 1st January, 2013 to 31st July, 2018) of 105 patients who were diagnosed with hypertension and received at least one treatment-related to hypertension in the hospital where death is the event of interest. It was reported by Umeh & Ibenegbu,[27] and used by Enogwe et al[28]. The data is shown below.…”

On the Statistical Properties of the Remkan Distribution

“…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]).…”

Iwueze’s Distribution and Its Application

“…The survivorship or existence measurement function (known as survival rate function [20] [21] [22]) is specified as ( ) , h v θ and average residual measurement life-time function (also known as mean residual life function [8] [21] [24]) is specified as…”