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

Abstract 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.   Abstrak Pada 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

Statistical Properties and Application of Bagui-Liu-Zhang Distribution

This paper extended the work of Bagiu et al. (2020) who defined the probability density function of a new oneparameter continuous distribution through the moment generating function approach. The new distribution called Bagiu-LiuZhang distribution is the distribution of the exponential mixture of the shifted exponential random variable. Properties ofthe distribution such as its cumulative distribution function (cdf), moments, coefficients of skewness and kurtosis,reliability function and hazard rate function were derived. The maximum likelihood estimator of the model parameter was also determined. We illustrated the usefulness of the distribution by comparing its fit to a real data set to the fit of the exponentialdistribution to the same data. The numericalresults obtained indicate that thedistribution can be a more suitable model forsome continuous data than the exponentialdistribution and several one-parameterdistributions

A New Family of Smooth Transition Autoregressive (STAR) Models: Properties and Application of its Symmetric Version to Exchange Rates

Communication in Physical Sciences, 2023, 9(3):310-324  Authors: Benjamin* Asuquo Effiong, Emmanuel Wilfred Okereke, Chukwuemeka Onwuzuruike Omekara, Chigozie Kelechi Acha and Emmanuel Alphonsus Akpan Received: 12  May 2023/Accepted 08 July 2023 A good number of economic variables undergo the process of regime shifts. In modeling such variables, it is necessary to consider a model that has provision for the regime form of nonstationarity. The smooth transition autoregressive (STAR) model is a choice model for time series with regime shifts. Given the role of transition functions in the performance of STAR models, this study introduced a family of transition functions by modifying the conventional logistic function. This new family, called the power logistic transition function, has the symmetric transition function and asymmetric transition function as special cases, making it useful in constructing both symmetric and asymmetric STAR models. The symmetric form of the family and the associated STAR model are extensively explained. The performance of the symmetric version of the power logistic smooth transition autoregressive model was illustrated with a monthly exchange rate of naira to United States dollar and African Financial Community Franc spanning from January 2004 to April 2021, which were extracted from Central Bank of Nigeria statistical bulletin. The numerical results obtained show that the symmetric power logistic smooth transition autoregressive model outperforms the linear autoregressive model and other existing symmetric smooth transition autoregressive models