This paper deals with studying a weighted exponential distribution with two parameters ( )
shape parameter ( ) and ( ) scale parameter ( ), and deriving itâs cumulative distribution function,
reliability function, also deriving the estimators by maximum likelihood method and moment estimator which are
found after deriving the moment generating function and obtaining . Also we try to use two
parameters ( ) as well as the reliability function using different sample size ( ),
comparison has been done using mean square error, all results explained by tables.
Keywords: Weighted exponential distribution, scale and shape parameters, cumulative distribution function,
reliability function, MLE, MOM.
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