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Estimation of the Probability Density Function of Lomax Distribution

Parmil Kumar, Kirandeep Kour, Jaspreet Kour

Abstract


Parameter estimation plays a critical role in accurately describing system behaviour through mathematical models such as Statistical Probability distribution functions.The Lomax distribution has been used in a various fields. It was originally introduced for modelling business failure data but now the Lomax distribution has been used for reliability modelling and life testing. It has a wide use in business, economics, and actuarial modelling. In this paper, we have estimated the Maximum Likelihood Estimators (MLE) and UMVUE of the shape parameter as well as pdf of the Lomax Distribution. Also, we have derived espressions for MSE for MLE and UMVUE of the pdf to find out which estimator is better. We have simulated the results using MatLab and presented them graphically too.

Keywords


Lomax distribution, Maximum Likelihood Estimator (MLE), Uniformly Minimum Variance Unbiased Estimator(UMVUE), Mean Square Error(MSE), Probability Density Function.

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