Abstract
In this paper the two-parameter
α
-power exponential distribution is studied. We study the two-parameter
α
-power exponential
μ
,
λ
distribution with the location parameter
μ
>
0
and scale parameter
λ
>
0
under progressive Type-II censored data with fixed shape parameter
α
. We estimate the maximum likelihood estimators of these unknown parameters numerically since it cannot be solved analytically. We use the approximate best linear unbiased estimators
μ
∗
and
λ
∗
, as an initial guesses to obtain the MLEs
μ
^
and
λ
^
. We estimate the interval estimation of these unknowns’ parameters. Monte Carlo simulations are performed and data examples have been provided for illustration and comparison.