<strong>ملخص الدراسة:</strong>

This paper deals with constructing a new probability distribution used for length biased data, which can be employed in development of proper model that use for data come for population which are size biased distribution, here we use the method to adjust the original distribution function from real data, and expectation of those data. The constructed distribution is called weighted exponential – Pareto (WEPD). The researcher work on construction the ( p.d.f ), C.D.F of this distribution, also deriving the general form of non-central and central moment (r^th moments about origin, and about μ), also the derivation of C.D.F need integration by incomplete Gamma formula. The r^th central moment formula is necessary for finding coefficient of Skewness and Kurtosis, which are used as a tool of some numerical method applied maximum likelihood estimators, and proposed estimators based on Cran's estimators. The last method is L – moment estimators, the comparison has been done through simulation using different values of sample size (n=40,80,100,150), the estimators were compared using MSE, MAPE ,all the results are explained in tables .Keywords: biased sized distribution, WEPD, incomplete Gamma, maximum likelihood, maximum entropy, L – moment, Cran's estimator, MSE, MAPE. This paper represent a sub – research taken from Ph.D thesis submitted to the department of statistics / college of administration and economic / University of Baghdad, Iraq.

ملخص الدراسة:

This paper deals with constructing a new probability distribution used for length biased data, which can be employed in development of proper model that use for data come for population which are size biased distribution, here we use the method to adjust the original distribution function from real data, and expectation of those data. The constructed distribution is called weighted exponential – Pareto (WEPD). The researcher work on construction the ( p.d.f ), C.D.F of this distribution, also deriving the general form of non-central and central moment (r^th moments about origin, and about μ), also the derivation of C.D.F need integration by incomplete Gamma formula. The r^th central moment formula is necessary for finding coefficient of Skewness and Kurtosis, which are used as a tool of some numerical method applied maximum likelihood estimators, and proposed estimators based on Cran’s estimators. The last method is L – moment estimators, the comparison has been done through simulation using different values of sample size (n=40,80,100,150), the estimators were compared using MSE, MAPE ,all the results are explained in tables .Keywords: biased sized distribution, WEPD, incomplete Gamma, maximum likelihood, maximum entropy, L – moment, Cran’s estimator, MSE, MAPE. This paper represent a sub – research taken from Ph.D thesis submitted to the department of statistics / college of administration and economic / University of Baghdad, Iraq.