Confıdence Intervals And Comparısons Based On Absolute Devıatıon For Populatıon Mean Of A Posıtıvely Skewed Dıstrıbutıon

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Thesis Type: Postgraduate

Institution Of The Thesis: Gazi University, Fen Bilimleri Enstitüsü, İSTATİSTİK ANABİLİM DALI, Turkey

Approval Date: 2020

Thesis Language: Turkish

Student: ZELİHA TÜRKMEN

Supervisor: HAMZA GAMGAM

Open Archive Collection: AVESIS Open Access Collection

Abstract:

It is quite common to use the classical confidence interval method based on the Student-t distribution for population mean. However, this confidence interval method does not give good results for a positively skewed populations when the assumption of normality is not provided. In this study, three confidence interval methods named AADM-t, MAAD-t and MADM-t are introduced. These confidence interval methods for population mean are created with simple adjustments in the confidence interval method based on the Student-t distribution. A simulation study was performed for the performances of these confidence interval methods. In this simulation study, data generated from Gamma, Beta, Lognormal, Chi-square and Weibull distributions with different skewness coefficients were used. These confidence interval methods were compared according to the coverage probability and average range width criteria. Simulation results revealed that the coverage probabilities for the classical confidence interval and AADM-t confidence interval methods are close to the nominal confidence level, but these probabilities of the MAAD-t and MADM-t confidence interval methods are quite different from the nominal confidence level. On the other hand, although the MADM-t confidence interval method has narrower average range widths than others, it is quite bad in terms of coverage probabilities