Confidence Intervals For The Common Variance Of Lognormal Distributions

Narudee Smithpreecha; Suparat Niwitpong

doi:https://doi.org/10.14445/22315373/IJMTT-V66I1P517

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 66 | Issue 1 | Year 2020 | Article Id. IJMTT-V66I1P517 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I1P517

Confidence Intervals For The Common Variance Of Lognormal Distributions

Narudee Smithpreecha , Suparat Niwitpong

Citation :

Narudee Smithpreecha , Suparat Niwitpong, "Confidence Intervals For The Common Variance Of Lognormal Distributions," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 1, pp. 135-147, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I1P517

Abstract

The aim of this paper is to investigate constructing confidence intervals for the common variance of lognormal distributions using four approaches, namely the generalized confidence intervals approach (GCI), the large sample approach (LS) and the adjusted method of variance estimates recovery approach (Adjusted MOVER) based on cox’s method (AM-Cox) and based on Angus’s conservative method (AM- Angus). The natural logarithm transformation was used to change the data to a normal distribution. The proposed intervals were evaluated focusing on coverage probability and average length using a Monte Carlo simulation. The results showed that the AM- Angus approach performs well in terms of coverage probability, but the average length was wide. Moreover, the coverage probability of the AM-Cox approach was closer to the nominal level more than the GCI approach. All approaches are illustrated using two real data examples.

Keywords

Common variance, Lognormal distribution, Generalized confidence interval, Large sample approach, Adjusted method of variance estimates recovery

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