Different Methods for Estimating the Parameters and Estimating the PDF and the CDF

In this paper, we consider the estimation of the probability density function (PDF) and the cumulative distribution function (CDF) of the Laplace distribution. In this regard, the following estimators are considered: uniformly minimum variance unbiased (UMVUE) estimator, maximum Likelihood (ML) estimator, percentile (PC) estimator, least squares (LS) estimator and weighted least squares (WLS) estimator. To do so, analytical expressions are derived for the bias and the mean squared error. As the result of simulation studies and real data applications indicate, the ML estimator performs better than the others.

کلیدواژه ها:

Laplace distribution ، maximum likelihood estimator ، percentile estimator ، uniform minimum variance unbiased estimator ، weighed least squares estimator