Exact distributions and interval estimation of the parameters of double exponential (Laplace) population for a small number of observations

In the article exact joint and marginal distributions for the location and scale parameters of the double exponential (Laplace) population for a number of observations from n = 2 up to n = 10 are given. These distributions are obtained by transformation of the joint distribution of estimators. It sown that the basic problem of the deriving the joint distribution of estimators relate with the presence of module functions in the model of the population distribution. The general procedures to derive the joint distribution of estimators for the odd and even number of observations are presented. The expected values, variances, standard deviations (uncertainties) and two-side confidence intervals of population parameters for a confidence levels p = 0.90, 0.95 and 0.99 are determined and presented in corresponding tables. The obtained results were verified by Monte-Carlo simulations.

Automated summary

This article examines the joint and marginal distributions for the location and scale parameters of the double exponential (Laplace) population for different numbers of observations. By transforming the joint distribution of estimators, the distributions are obtained, with the presence of module functions in the population distribution model being a key issue. General procedures for deriving the joint distribution of estimators for odd and even numbers of observations are introduced, along with calculations for expected values, variances, uncertainties, and confidence intervals for population parameters at various confidence levels. The results obtained were validated through Monte-Carlo simulations.