Page 382 - Contributed Paper Session (CPS) - Volume 6

CPS1992 Epimaco A. Cabanlit, Jr. et al.

On the mixture of two power function
distributions
Epimaco A. Cabanlit, Jr., Mycah Shaene R. Nailon
Mindanao State University, General Santos City, Philippines

Abstract
The mixture of distributions can serve as a model to some realities where the
population consists of heterogeneous components. The mixture of two power
function distributions provides a mathematical-based approach to the
statistical modelling of data. This paper presents some of the important
summaries of the mixture of two power function distributions such as the
mean, variance, and rth moment about the origin.

Keywords
power function distributions; Mixture of distributions; Summaries of
Distribution

1. Introduction
A suitable generalized lifetime model is often of interest in the analysis of
survival data, as it can provide insight into characteristics of failure times and
hazard functions that may not be available with classical models. Four
distributions, Exponential, Pareto, Power and Weibull, are of interest and very
attractive in lifetime literature due to their simplicity, easiness and flexible
features to model various types of data in different fields (Cordeiro, et al.,
2012). Exponential distribution is a distribution of the time to an event when
the probability of the event occurring in the next small time interval does not
vary through time. Pareto distribution is often described as the basis of the
80/20 rule. Weibull distribution can represent decreasing, constant, or
increasing failure rates (Forbes, C., et al., 2011). Power distribution can be used
to fit the distribution of certain likelihood ratios in statistical tests and it can
be used to compare two tests which have the same significance level
(Cordeiro, et al., 2012).
Meniconi and Barry (1995) discussed the application of the power function
distribution (PFD) along with other lifetime models, and concluded that the
PFD is better than the Weibull, log-normal and exponential models to measure
the reliability of any electrical component. The use of exponential, Weibull, and
log-normal, which are frequently preferred over mathematically more complex
distribution, suggests that most engineers favour the application of simpler
models to obtain failure rates and reliability figures quickly. It is therefore
proposed that the power function distribution be considered as a simple

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