Abstract
Accurate estimation of parameters of a probability distribution is of immense importance in statistics. Biased and imprecise estimation of parameters can lead to erroneous results. Our focus is to estimate the parameter of Power function distribution accurately because this density is now widely used for modelling various types of data. In this study, L-moments, TL-moments, LL-moments and LH-moments of Power function distribution are derived. In addition, the coefficient of variation, skewness and kurtosis are obtained by method of moments, L-moments and TL-moments. Parameters of the density are estimated using linear moments and compared with method of moments and MLE on the basis of bias, root mean square error and coefficients through simulation study. L-moments proved to be superior for the parameter estimation and this conclusion is equally true for different parametric values and sample size.
Highlights
The Power Function Distribution (PFD) is a flexible distribution as it is able to model the various types of data
Expressions of the first four linear moments, coefficient of variation (CV), Sk and Kr are derived for PFD
Parameters are estimated by MM, LM, Trimmed L- moments (TLM) and Maximum likelihood estimation (MLE) and following interesting results have been observed from the simulation study
Summary
The Power Function Distribution (PFD) is a flexible distribution as it is able to model the various types of data It is usually used for the reliability analysis, life time and income distribution data. Meniconi & Barry (1996) compare the PFD with Exponential, Lognormal and Weibull distribution to measure the reliability of electrical components They conclude that the PFD is the best distribution to model such types of data. Linear moments of PFD are not discussed before in the literature according to our knowledge We have derived these moments and compared their performance with traditional methods.
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