Confidence interval estimation of the ratio of means and medians of lognormal distributions with applications

Name: Lapasrada Singhasomboon

keyword: Lognormal distribution

; Confidence/credible intervals

; Ratio of lognormal means

; Ratio of lognormal medians

; Approximate method

; Bayesian method

; Normal approximation

; Non-informative prior assumption

; Normal-gamma conjugate prior

; Coverage probability

; Average length

Abstract: The lognormal distribution is used extensively to describe the distribution of positive random variables and also frequently utilized in many applications. The main purpose in this research is to construct the confidence/credible intervals (CIs) of the ratio of means and medians of two independent lognormal distributions based on the approximate and Bayesian methods and investigate their performance. For the theoretical part, in constructing the CIs of the ratio of means of the lognormal distributions, the approximate method, namely, the normal approximation method and the Bayesian method based on normal-gamma conjugate prior are proposed. The performances of the proposed will be compared in the computational part with the existing methods such as the maximum likelihood (ML) studied by Zhou et al. (1997), generalized confidence interval (GCI) studied by Krishnamoorthy and Mathew (2003), the method of variance estimates recovery (MOVER) studied by Abdel-Karim (2012), as well as Bayesian CIs based on Independence Jeffreys’, Jeffreys’ rule, and uniform priors. Latter are the Bayesian methods using non-informative prior assumption studied by Harvey and Merwe (2010, 2012). Next, similar to constructing CIs for the ratio of lognormal means, the procedures for obtaining CIs for the ratio of medians of lognormal distributions such as the approximate CI based on normal approximation and the Bayesian CI based on normal-gamma conjugate prior are proposed and also compared with the existing methods. However, the existing methods based on approximate and Bayesian methods constructed for CIs of the ratio of lognormal medians have not been studied in the literature review. Only the Bayesian CIs such as the CIs based on the Independence Jeffreys’, Jeffreys’ rule, and uniform priors for a single lognormal median proposed by Rao and D’Canha (2016) were considered. Thus, to compare with the CIs purposed in this study, the ML proposed by Zhou et al. (1997), the GCI proposed by Krishnamoorthy and Mathew (2003), the MOVER proposed by Abdel-Karim (2012) are modified to obtain the CIs for the ratio of lognormal medians. Moreover, the CIs based on the independence Jeffreys’, Jeffreys’ rule, and uniform priors for a single lognormal median proposed by Rao and D’Canha (2016) are extended to obtain the CIs for the ratio of lognormal medians also. In the computational part, a simulation is conducted to compare the performance of all methods. Their performances are compared under various parameter combinations of the two independent lognormal distributions in terms of coverage probability and average length using Monte Carlo simulation. The PM2.5 data from Bangkapi and Dindaeng areas in Thailand is used to confirm the effectiveness of the proposed methods. It is found the result outstandingly agreed with the real data

Thammasat University. Thammasat University Library

Address: BANGKOK

Email: preserv@tu.ac.th

Name: Wararit Panichkitkosolkul

Role: advisor

Name: Volodin, Andrei Igorevich

Role: co-advisor

Created: 2021

Modified: 2023-02-09

Issued: 2023-02-09

วิทยานิพนธ์/Thesis

application/pdf

DOI: 10.14457/TU.the.2021.47

eng

DegreeName: Doctor of Philosophy

Level: Doctoral Degree

Descipline: Statistics

Grantor: Thammasat University

©copyrights Thammasat University

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