Alpha power transformed Pareto distribution and its properties with application

K.M., Sakthivel; A., Arul chezhian

doi:10.26637/mjm0s20/0011

Cited by 4 publications

(4 citation statements)

References 13 publications

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“…In the literature, some univariate probability distributions have been generalized using this Alpha Power Transformation method. Some of these distributions include the Alpha power transformed (APT) Pareto distribution (see [13]), the APT Lindley distribution (see [14]), the APT Weibull-G family of distributions (see [15]), the APT inverse Lomax distribution (see [16]) and APT log-logistic distribution (see [17]). To the best of our knowledge, this alpha power transformation technique is yet to be used to generalize the logistic distribution.…”

Section: Var X Fmentioning

confidence: 99%

The Alpha Power Transformed Logistic Distribution: Properties, application and VaR Estimation

Iwuji

Okereke

Oruh

et al. 2023

InPrime:Ind.Jour.Pure.Applied.Math

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In this paper, a new three-parameter distribution, which is a member of the Alpha Power Transformed Family of distributions, is introduced. The new distribution is a generalization of the logistic model called the alpha power transformed logistic (APTL) distribution. Some mathematical properties of the new distribution like moments, quantile function, median, skewness, kurtosis, Rényi entropy, and order statistics are discussed. The parameters of the distribution are estimated using the maximum likelihood estimation method and a simulation study is performed to investigate the effectiveness of the estimates. The usefulness and flexibility of the APTL distribution in modelling financial data are investigated using two portfolio stock indices, namely the NASDAQ and New York stock indices, both from the United States stock market. Based on the model selection criteria, we are able to establish empirically that the APTL distribution is the best for modelling the two data sets, among the various distributions compared in the study. For each of the data, the quantile value-at-risk estimates for the APTL distribution give the smaller expected portfolio loss at high confidence levels in comparison to those of the other distributions.Keywords: Alpha power transformed family of distributions; logistic distribution; maximum likelihood estimation; portfolio investments; value-at-risk. AbstrakPada artikel ini, diperkenalkan distribusi baru dengan tiga parameter yang merupakan anggota dari keluarga distribusi Alpha Power Transformed. Distribusi baru ini merupakan generalisasi dari model logistik yang disebut distribusi Alpha Power Transform Logistics (APTL). Selain itu, dibahas pula beberapa sifat matematika dari distribusi tersebut yaitu momen, fungsi kuantil, median, kemiringan, kurtosis, entropi Rényi, dan statistik terurut. Parameter distribusi diestimasi menggunakan metode maximum likelihood estimation dan studi simulasi dilakukan untuk menyelidiki keefektifan estimasi. Kegunaan dan fleksibilitas distribusi APTL dalam pemodelan data keuangan diselidiki menggunakan dua indeks saham portofolio dari pasar saham Amerika Serikat yaitu indeks saham NASDAQ dan New York. Berdasarkan kriteria pemilihan model, secara empiris, dihasilkan bahwa APTL adalah distribusi terbaik untuk memodelkan dua set data di antara berbagai distribusi yang dibandingkan pada penelitian ini. Untuk setiap data, estimasi kuantil value-at-risk untuk distribusi APTL memberikan kerugian portofolio yang diharapkan lebih kecil dengan tingkat kepercayaan tinggi dibandingkan dengan distribusi lainnya.Kata Kunci: distribusi dari keluarga Alpha power transformed; distribusi logistik; maximum likelihood estimation; investasi portofolio; value-at-risk. 2020MSC: 62E10.

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Section: Var X Fmentioning

confidence: 99%

The Alpha Power Transformed Logistic Distribution: Properties, application and VaR Estimation

Iwuji

Okereke

Oruh

et al. 2023

InPrime:Ind.Jour.Pure.Applied.Math

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“…Te authors of [20] introduced a new method by adding an additional parameter called the alpha power transformation (APT) family. Te APT family has been used to develop several modifed distributions, including the APT Fréchet [21], APT extended exponential distribution [22], APT inverse Lomax distribution [23], APT log-logistic distribution [24], APT inverse Lindley distribution [25], and APT Pareto distribution [26], among others. With the aim of improving the fexibility of the APT family of distributions, Alotaibi et al [27] modifed the APT family of distributions and obtained a new family of distributions called the modifed alpha power transformed method (MAPT).…”

Section: Introductionmentioning

confidence: 99%

New Weighted Burr XII Distribution: Statistical Properties, Applications, and Regression

Anafo,

Ocloo,

Nasiru

2024

International Journal of Mathematics and Mathematical Sciences

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In this study, a three-parameter modification of the Burr XII distribution has been developed through the integration of the weighted version of the alpha power transformation family of distributions. This newly introduced model, termed the modified alpha power-transformed Burr XII distribution, exhibits the unique ability to effectively model decreasing, right-skewed, or unimodal densities. The paper systematically elucidates various statistical properties of the proposed distribution. The estimation of parameters was obtained using maximum likelihood estimation. The estimator has been evaluated for consistency through simulation studies. To gauge the practical applicability of the proposed distribution, two distinct datasets have been employed. Comparative analyses involving six alternative distributions unequivocally demonstrate that the modified alpha power-transformed Burr XII distribution provides a better fit. Additionally, a noteworthy extension is introduced in the form of a location-scale regression model known as the log-modified alpha power-transformed Burr XII model. This model is subsequently applied to a dataset related to stock market liquidity. The findings underscore the enhanced fitting capabilities of the proposed model in comparison to existing distributions, providing valuable insights for applications in financial modelling and analysis.

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“…In the literature, a lot of work has been done by using APT technique, such as (12) defined Alpha Power transformed power lindely distribution, (13) obtained Alpha Power transformed inverse lindely distribution, (14) suggested Alpha Power inverse Weibull distribution, (15) introduced Alpha Power transformed Frechet distribution, (16) proposed Alpha Power transformed inverse lomax distribution, (17) discussed Alpha Power transformed Pareto distribution, (18) obtained Alpha Power transformed Aradhana distribution, (19) studied Alpha Power transformation of lomax distribution, (20) introduced Alpha Power Two-Parameter Pranav distribution.The aim of this article is to introduce and study a new three parameter alpha power transformation of (TPO) distribution called the alpha power two parameter odoma (APTPO) distribution and proposed some special cases of it. Some properties of the new distribution including the shapes of density function and hazard rate function, quantile function, moments and moment generating function, incomplete moment, and Lorenz and Bonferroni curves are discussed.…”

Section: Introductionmentioning

confidence: 99%

New Odoma Distribution with Application to Cancer Data

Abdelall¹

2023

IJST

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Objective: To find appropriate model more flexible than classical models for fitting the survival data in health research especially in cancer blood (Leukemia) studies by introducing some additional parameters to the basic models. Methods: Based on the Alpha Power transformation technique and using Two-Parameter Odoma distribution, the new distribution called the Alpha Power Two-Parameter Odoma distribution is introduced and studied. The maximum likelihood estimation procedure is employed to estimate the unknown parameters. A simulation study is carried out to evaluate the performance of the maximum likelihood estimators. Finding: Common statistical properties such as quantile function, rth moments, moment generating function, characteristic function, incomplete moments, entropy and order statistics are derived. The practical importance of the proposed model is illustrated by using goodness-of-fit criterias based on real data set. Novelty: The APTPO distribution is the most appropriate model for fitting survival data of cancer studies comparing with other competitive distributions.

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Alpha power transformed Pareto distribution and its properties with application

Cited by 4 publications

References 13 publications

The Alpha Power Transformed Logistic Distribution: Properties, application and VaR Estimation

The Alpha Power Transformed Logistic Distribution: Properties, application and VaR Estimation

New Weighted Burr XII Distribution: Statistical Properties, Applications, and Regression

New Odoma Distribution with Application to Cancer Data

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