The Length-Biased Weighted Erlang Distribution
Hesham M. Reyad *
College of Business and Economics, Qassim University, Kingdom of Saudi Arabia.
Soha A. Othman
Institute of Statistical Studies and Research, Cairo University, Egypt.
Alaaeddin A. Moussa
College of Business and Economics, Qassim University, Kingdom of Saudi Arabia.
*Author to whom correspondence should be addressed.
Abstract
We introduce and study a new continuous model so called, the length-biased weighted Erlang (LBWE) distribution. Some mathematical properties of the new distribution such as, raw and incomplete moments, generating functions, Rényi of entropy, order and record statistics are investigated. The moments and maximum likelihood estimates are obtained for the model parameters. An application to real data set is used to illustrate the usefullness of the new model.
Keywords: Erlang distribution, weighted distribution, maximum likelihood estimation, moments estimation, order statistics, record statistics