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

Mehdi Baluoi¹ Einolah Deiri² Seyede Safora Hoseyni³

1) Department of Statistics, Khouzestan Science and Research Branch, Islamic Azad University, Email Ahvaz, Iran
2) Department of mathematical and statistics , Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran
3) M.s.c in statictic, pyamnor uneversity,tehran,Iran

Publication : 3rd International Congress on Science, engineering & New Technologies(secongress.com)
Abstract :
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.
Keywords : laplace distribution maximum likelihood estimator percentile estima tor uniform minimum variance unbiased estimator weighed least squares estimator