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In this paper a useful subfamily of the exponential family has been considered. The ML estimation based on upper record values has been calculated for the parameter, Cumulative Density Function, and Probability Density Function of the family. Also, the relations between MLE based on record values and a random sample has been discussed. Additionally, some properties of these estimators have been investigated. Finally, it has been proven that these estimators have some useful properties for samples with large size

journal of modern applied statistical methods

Maximum Likelihood Estimations Based on Upper Record Values for Probability Density Function and Cumulative Distribution Function in Exponential Family and Investigating Some of Their Properties