Maximum Likelihood Estimation for Generalized Power Series Distributions and Its Application to a Truncated Binomial Distribution

Biometrika ◽  
1962 ◽  
Vol 49 (1/2) ◽  
pp. 227 ◽  
Author(s):  
G. P. Patil
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Power Series ◽  
Binomial Distribution ◽  
Likelihood Estimation ◽  
Generalized Power Series ◽  
Power Series Distributions

scholarly journals The Exponentiated Burr XII Power Series Distribution: Properties and Applications

Stats ◽  
2018 ◽  
Vol 2 (1) ◽  
pp. 15-31
Author(s):  
Arslan Nasir ◽  
Haitham Yousof ◽  
Farrukh Jamal ◽  
Mustafa Korkmaz
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Power Series ◽  
Likelihood Estimation ◽  
Real Data ◽  
Estimation Procedure ◽  
Model Parameters ◽  
Data Sets ◽  
Power Series Distributions ◽  
New Distribution

In this work, we introduce a new Burr XII power series class of distributions, which is obtained by compounding exponentiated Burr XII and power series distributions and has a strong physical motivation. The new distribution contains several important lifetime models. We derive explicit expressions for the ordinary and incomplete moments and generating functions. We discuss the maximum likelihood estimation of the model parameters. The maximum likelihood estimation procedure is presented. We assess the performance of the maximum likelihood estimators in terms of biases, standard deviations, and mean square of errors by means of two simulation studies. The usefulness of the new model is illustrated by means of three real data sets. The new proposed models provide consistently better fits than other competitive models for these data sets.

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