Exact prediction intervals for order statistics from the Laplace distribution based on the MLEs
G. Iliopoulos and S.M.T.K. MirMostafaee
In this work we construct exact prediction intervals for order statistics from the
Laplace (double exponential) distribution. We consider both the one- and two-sample
prediction cases. The intervals are based on certain pivotal quantities that employ
the corresponding maximum likelihood predictors and the predictive maximum likelihood
estimators of the unknown parameters. Similarly to Iliopoulos and Balakrishnan
(2011), we express the distributions of the pivotal quantities as mixtures of ratios of
linear combinations of independent standard exponential random variables. Since
these distributions are in closed form we solve numerically the corresponding equations
and obtain their exact quantiles. Tables containing selected quantiles of the
pivotal quantities are provided. Numerical examples are also given for illustration
purposes.
Key words and phrases: Laplace distribution; exact prediction intervals; predictive
likelihood function; maximum likelihood estimators; ratios of linear combinations of exponential
random variables.
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