M-Estimations of Shape and Scale Parameters by Order Statistics in Least Informative Distributions on q-deformed logarithm

Mehmet Niyazi ÇANKAYA

doi:https://doi.org/10.21597/jist.720712

Makale detayları

M-Estimations of Shape and Scale Parameters by Order Statistics in Least Informative Distributions on q-deformed logarithm

Yazarlar:

Mehmet Niyazi ÇANKAYA

Yayıncı:

Igdir University

Ana Başlıklar:

Matematik

Dergi:

Journal of the Institute of Science and Technology 2020 Vol.10 Issue 3, pp.1984-1996

Belge Tipi:

Makale

Yayın Tarihi:

8/2020

Belge Dili:

İngilizce

Document ID (Org No.):

2000463883

Sıklık:

Üç Aylık

eISSN:

2536-4618

DOI:

https://doi.org/10.21597/jist.720712

Özet:

 

The maximum logq likelihood estimation (MLqE) method is used to estimate robustly parameters recently. In robust estimation method, the least informative distribution (LID) proposed by Huber is a convex combination of two probability density functions 0 and 1. In this study, the recently proposed least informative distributions (LIDs) in MLqE are used to estimate parameters. This paper also studies on the objective functions proposed by maximum logq-likelihood principle (MLqE) originally derived by logq-likelihood. The role and capability of order statistics in LIDs in MLqE are examined while getting the estimates of shape and scale parameters. The distance measure for evaluation of fitting performance is given to choose a value for the parameter  in logq when the objective functions derived from MLqE are used. The simulation and real data application are given. Thus, we compare the fitting performance of objective functions constructed by MLE on log, MLqE on logq and LIDs with order statistics in MLqE. We observed that order statistic chosen for density 1 in LID in MLqE has a new objective function to fit the data sets. In the simulation, we make two contaminations into artificial data sets. The first contamination is inliers derived by order statistics and the second one is outliers. Thus, we observe that the new objective function can give satisfactory results.

 

The maximum logq likelihood estimation (MLqE) method is used to estimate robustly parameters recently. In robust estimation method, the least informative distribution (LID) proposed by Huber is a convex combination of two probability density functions 0 and 1. In this study, the recently proposed least informative distributions (LIDs) in MLqE are used to estimate parameters. This paper also studies on the objective functions proposed by maximum logq-likelihood principle (MLqE) originally derived by logq-likelihood. The role and capability of order statistics in LIDs in MLqE are examined while getting the estimates of shape and scale parameters. The distance measure for evaluation of fitting performance is given to choose a value for the parameter  in logq when the objective functions derived from MLqE are used. The simulation and real data application are given. Thus, we compare the fitting performance of objective functions constructed by MLE on log, MLqE on logq and LIDs with order statistics in MLqE. We observed that order statistic chosen for density 1 in LID in MLqE has a new objective function to fit the data sets. In the simulation, we make two contaminations into artificial data sets. The first contamination is inliers derived by order statistics and the second one is outliers. Thus, we observe that the new objective function can give satisfactory results.

Makale detayları

M-Estimations of Shape and Scale Parameters by Order Statistics in Least Informative Distributions on q-deformed logarithm

Yazarlar: Mehmet Niyazi ÇANKAYA

Yayıncı: Igdir University

Ana Başlıklar: Matematik

Dergi: Journal of the Institute of Science and Technology 2020 Vol.10 Issue 3, pp.1984-1996

Belge Tipi: Makale

Yayın Tarihi: 8/2020

Belge Dili: İngilizce

Document ID (Org No.): 2000463883

Sıklık: Üç Aylık

eISSN: 2536-4618

DOI: https://doi.org/10.21597/jist.720712

Sayı

Yazarlar:

Mehmet Niyazi ÇANKAYA

Yayıncı:

Igdir University

Ana Başlıklar:

Matematik

Dergi:

Journal of the Institute of Science and Technology 2020 Vol.10 Issue 3, pp.1984-1996

Belge Tipi:

Makale

Yayın Tarihi:

8/2020

Belge Dili:

İngilizce

Document ID (Org No.):

2000463883

Sıklık:

Üç Aylık

eISSN:

2536-4618

DOI:

https://doi.org/10.21597/jist.720712