Συμπερασματολογία για τις παραμέτρους της κατανομής Laplace
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Keywords
Κατανομή Laplace ; Διαφορά παραμέτρων θέσης ; Ακριβείς έλεγχοι ; Ακριβή διαστήματα εμπιστοσύνης ; Λόγος παραμέτρων κλίμακας ; Αμερόληπτοι έλεγχοι ; Αμερόληπτα διαστήματα εμπιστοσύνηςAbstract
The subject of this PhD thesis is in the field of Mathematical Statistics. First there is a presentation of Laplace distribution and its properties. Known general results concerning order statistics from independent samples are presented. In particular, there are also results in the case where the parent distribution is exponential. Moreover, new results concerning order statistics from the Laplace distribution are proved.
The main results of the PhD thesis concerning the comparison of the location parameters of two populations from Laplace distribution follow. Exact tests for the comparison of the location parameters of two Laplace distributions with common yet unknown scale parameter based on corresponding independent samples are constructed. The likelihood ratio test statistic and the scaled difference of the best linear unbiased estimators of the parameters are considered. By conditioning on certain quantities, the exact distributions of the test statistics are expressed as mixtures of ratios of linear combinations of standard exponential random variables. Exact quantiles are found and exact confidence intervals are constructed for the difference of the means as well. The tests are numerically compared via their power.
The comparison of the scale parameters of two populations from Laplace distribution follows. More specifically, exact tests for the comparison of the scale parameters of two Laplace distributions based on corresponding independent samples are constructed. The likelihood ratio test statistic, the ratio of the maximum likelihood estimators and the ratio of the best linear unbiased estimators of the parameters are considered. Following the same procedure as in the case of the comparison of the location parameters their exact distributions and their exact quantiles are presented. Unbiased tests and unbiased confidence intervals are constructed numerically. The tests are numerically compared via their power.