Estimasi Parameter Μ Dan Σ2 pada Distribusi Eksponensial Tergeneralisir Dua Variabel Menggunakan Fungsi Pembangkit Momen

Abstract

From some distribution, the mean and variance is an important parameter estimates after the parameters distribution are known. From estimates of these parameters we can more easily review, investigate the characteristics, and found all of other measurement parameters such as skewness and kurtosis of these distribution. In estimating these parameters correctly, the most appropriate method used is the moment generating function.Obvious usefulness from the moment generating function is to determine the moment of it’s distribution. If the moment generating function of a random variable exists, the function can be used to transform and find all the moments of these random variables, moment generating function by deriveded to n-times. Can be seen that the first derivative is average and the second derivative is the variance. For random variables X1 and X2 are continuous, then the joint moment generating function is denoted by: 21221121)()(),(221121dxdxxfxfettMxtxtxx+ In this research, distributions will be estimated parameter mean and variance is a new distribution introduced by Gupta and Kundu (1999), named a Generalized Exponential Distribution. If there are two random variables (X1,X2) a Generalized Exponential Distribution with the assumptions are mutually independent, then the Generalized Exponential distribution of two variables (joint probability density function of (X1,X2)), for x1 > 0, x2 > 0 is: ),(21xxF 2122111121)1()1(xxxxeee−−−−−−−−=αααα