scholarly journals Heavy-Tailed Log-Logistic Distribution: Properties, Risk Measures and Applications

2021 ◽  
Vol 9 (4) ◽  
pp. 910-941
Author(s):  
Abd-Elmonem A. M. Teamah ◽  
Ahmed A. Elbanna ◽  
Ahmed M. Gemeay
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Risk Measures ◽  
Real Data ◽  
Estimation Methods ◽  
Logistic Distribution ◽  
Model Parameters ◽  
Data Sets ◽  
Alpha Power ◽  
Heavy Tailed

Heavy tailed distributions have a big role in studying risk data sets. Statisticians in many cases search and try to find new or relatively new statistical models to fit data sets in different fields. This article introduced a relatively new heavy-tailed statistical model by using alpha power transformation and exponentiated log-logistic distribution which called alpha power exponentiated log-logistic distribution. Its statistical properties were derived mathematically such as moments, moment generating function, quantile function, entropy, inequality curves and order statistics. Five estimation methods were introduced mathematically and the behaviour of the proposed model parameters was checked by randomly generated data sets and these estimation methods. Also, some actuarial measures were deduced mathematically such as value at risk, tail value at risk, tail variance and tail variance premium. Numerical values for these measures were performed and proved that the proposed distribution has a heavier tail than others compared models. Finally, three real data sets from different fields were used to show how these proposed models fitting these data sets than other many wells known and related models.

scholarly journals The Extended Log-Logistic Distribution: Inference and Actuarial Applications

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1386
Author(s):  
Nada M. Alfaer ◽  
Ahmed M. Gemeay ◽  
Hassan M. Aljohani ◽  
Ahmed Z. Afify
Keyword(s):  
Hazard Function ◽  
Risk Measures ◽  
Real Data ◽  
Estimation Methods ◽  
Risk Exposure ◽  
Logistic Distribution ◽  
Alpha Power ◽  
Bathtub Shape ◽  
Simulation Results ◽  
Heavy Tailed

Actuaries are interested in modeling actuarial data using loss models that can be adopted to describe risk exposure. This paper introduces a new flexible extension of the log-logistic distribution, called the extended log-logistic (Ex-LL) distribution, to model heavy-tailed insurance losses data. The Ex-LL hazard function exhibits an upside-down bathtub shape, an increasing shape, a J shape, a decreasing shape, and a reversed-J shape. We derived five important risk measures based on the Ex-LL distribution. The Ex-LL parameters were estimated using different estimation methods, and their performances were assessed using simulation results. Finally, the performance of the Ex-LL distribution was explored using two types of real data from the engineering and insurance sciences. The analyzed data illustrated that the Ex-LL distribution provided an adequate fit compared to other competing distributions such as the log-logistic, alpha-power log-logistic, transmuted log-logistic, generalized log-logistic, Marshall–Olkin log-logistic, inverse log-logistic, and Weibull generalized log-logistic distributions.

scholarly journals The Alpha Power Transformation Family: Properties and Applications

2019 ◽  
pp. 525-545 ◽  
Author(s):  
Mohamed E. Mead ◽  
Gauss M. Cordeiro ◽  
Ahmed Z. Afify ◽  
Hazem Al Mofleh
Keyword(s):  
Real Data ◽  
Likelihood Method ◽  
Model Parameters ◽  
Power Transformation ◽  
Data Sets ◽  
Alpha Power ◽  
Weibull Distributions ◽  
Exponentiated Weibull ◽  
Rate Functions ◽  
Modified Weibull

Mahdavi A. and Kundu D. (2017) introduced a family for generating univariate distributions called the alpha power transformation. They studied as a special case the properties of the alpha power transformed exponential distribution. We provide some mathematical properties of this distribution and define a four-parameter lifetime model called the alpha power exponentiated Weibull distribution. It generalizes some well-known lifetime models such as the exponentiated exponential, exponentiated Rayleigh, exponentiated Weibull and Weibull distributions. The importance of the new distribution comes from its ability to model monotone and non-monotone failure rate functions, which are quite common in reliability studies. We derive some basic properties of the proposed distribution including quantile and generating functions, moments and order statistics. The maximum likelihood method is used to estimate the model parameters. Simulation results investigate the performance of the estimates. We illustrate the importance of the proposed distribution over the McDonald Weibull, beta Weibull, modified Weibull, transmuted Weibull and exponentiated Weibull distributions by means of two real data sets.

scholarly journals HALF LOGISTIC MODIFIED EXPONENTIAL DISTRIBUTION: PROPERTIES AND APPLICATIONS

2020 ◽  
pp. 276-287
Author(s):  
Arun Kumar Chaudhary ◽  
Vijay Kumar
Keyword(s):  
Exponential Distribution ◽  
Likelihood Estimation ◽  
Real Data ◽  
Least Square ◽  
Estimation Methods ◽  
Logistic Distribution ◽  
Model Parameters ◽  
Type I ◽  
Data Set ◽  
Von Mises

In this study, we have introduced a three-parameter probabilistic model established from type I half logistic-Generating family called half logistic modified exponential distribution. The mathematical and statistical properties of this distribution are also explored. The behavior of probability density, hazard rate, and quantile functions are investigated. The model parameters are estimated using the three well known estimation methods namely maximum likelihood estimation (MLE), least-square estimation (LSE) and Cramer-Von-Mises estimation (CVME) methods. Further, we have taken a real data set and verified that the presented model is quite useful and more flexible for dealing with a real data set. KEYWORDS— Half-logistic distribution, Estimation, CVME ,LSE, , MLE

scholarly journals A New Extended-X Family of Distributions: Properties and Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Mi Zichuan ◽  
Saddam Hussain ◽  
Anum Iftikhar ◽  
Muhammad Ilyas ◽  
Zubair Ahmad ◽  
...  
Keyword(s):  
Real Data ◽  
Model Parameters ◽  
Data Sets ◽  
Statistical Distributions ◽  
Reliability Engineering ◽  
Monte Carlo Simulation Study ◽  
Diverse Range ◽  
Heavy Tailed ◽  
Log Normal ◽  
Extended Weibull Distribution

During the past couple of years, statistical distributions have been widely used in applied areas such as reliability engineering, medical, and financial sciences. In this context, we come across a diverse range of statistical distributions for modeling heavy tailed data sets. Well-known distributions are log-normal, log-t, various versions of Pareto, log-logistic, Weibull, gamma, exponential, Rayleigh and its variants, and generalized beta of the second kind distributions, among others. In this paper, we try to supplement the distribution theory literature by incorporating a new model, called a new extended Weibull distribution. The proposed distribution is very flexible and exhibits desirable properties. Maximum likelihood estimators of the model parameters are obtained, and a Monte Carlo simulation study is conducted to assess the behavior of these estimators. Finally, we provide a comparative study of the newly proposed and some other existing methods via analyzing three real data sets from different disciplines such as reliability engineering, medical, and financial sciences. It has been observed that the proposed method outclasses well-known distributions on the basis of model selection criteria.

scholarly journals The Arcsine Exponentiated-X Family: Validation and Insurance Application

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-18 ◽  
Author(s):  
Wenjing He ◽  
Zubair Ahmad ◽  
Ahmed Z. Afify ◽  
Hafida Goual
Keyword(s):  
At Risk ◽  
Weibull Distribution ◽  
Value At Risk ◽  
Claims Data ◽  
Numerical Study ◽  
Model Parameters ◽  
Insurance Claims ◽  
Goodness Of Fit Test ◽  
Insurance Claims Data ◽  
Heavy Tailed

In this paper, we propose a family of heavy tailed distributions, by incorporating a trigonometric function called the arcsine exponentiated-X family of distributions. Based on the proposed approach, a three-parameter extension of the Weibull distribution called the arcsine exponentiated-Weibull (ASE-W) distribution is studied in detail. Maximum likelihood is used to estimate the model parameters, and its performance is evaluated by two simulation studies. Actuarial measures including Value at Risk and Tail Value at Risk are derived for the ASE-W distribution. Furthermore, a numerical study of these measures is conducted proving that the proposed ASE-W distribution has a heavier tail than the baseline Weibull distribution. These actuarial measures are also estimated from insurance claims real data for the ASE-W and other competing distributions. The usefulness and flexibility of the proposed model is proved by analyzing a real-life heavy tailed insurance claims data. We construct a modified chi-squared goodness-of-fit test based on the Nikulin–Rao–Robson statistic to verify the validity of the proposed ASE-W model. The modified test shows that the ASE-W model can be used as a good candidate for analyzing heavy tailed insurance claims data.

scholarly journals Marshall-Olkin Alpha Power Rayleigh Distribution: Properties, Characterizations, Estimation and Engineering applications

2021 ◽  
pp. 745-760
Author(s):  
Ehab Mohamed Almetwally ◽  
Ahmed Z. Afify ◽  
G. G. Hamedani
Keyword(s):  
Maximum Likelihood ◽  
Hazard Function ◽  
Real Data ◽  
Rayleigh Distribution ◽  
Estimation Methods ◽  
Data Sets ◽  
Alpha Power ◽  
Monte Carlo Simulation Study ◽  
Bootstrap Estimation ◽  
Proposed Model

In this paper, we introduce a new there-parameter Rayleigh distribution, called the Marshall-Olkin alpha power Rayleigh (MOAPR) distribution. Some statistical properties of the MOAPR distribution are obtained. The proposed model is characterized based on truncated moments and reverse hazard function. The maximum likelihood and bootstrap estimation methods are considered to estimate the MOPAR parameters. A Monte Carlo simulation study is performed to compare the maximum likelihood and bootstrap estimation methods. Superiority of the MOAPR distribution over some well-known distributions is illustrated by means of two real data sets.

Risk Asset Portfolio Choice Models under Three Risk Measures

2011 ◽  
Vol 204-210 ◽  
pp. 537-540
Author(s):  
Yu Ling Wang ◽  
Jun Hai Ma ◽  
Yu Hua Xu
Keyword(s):  
At Risk ◽  
Portfolio Choice ◽  
Value At Risk ◽  
Financial Risk ◽  
Risk Measures ◽  
Empirical Support ◽  
Real Data ◽  
Conditional Value At Risk ◽  
Asset Portfolio ◽  
Special Value

Mean-variance model, value at risk and Conditional Value at Risk are three chief methods to measure financial risk recently. The demonstrative research shows that three optional questions are equivalence when the security rates have a multivariate normal distribution and the given confidence level is more than a special value. Applications to real data provide empirical support to this methodology. This result has provided new methods for us about further research of risk portfolios.

scholarly journals On Modeling the Earthquake Insurance Data via a New Member of the T-X Family

2020 ◽  
Vol 2020 ◽  
pp. 1-20
Author(s):  
Zubair Ahmad ◽  
Eisa Mahmoudi ◽  
Omid Kharazmi
Keyword(s):  
At Risk ◽  
Maximum Likelihood ◽  
Simulation Study ◽  
Value At Risk ◽  
Model Parameters ◽  
Earthquake Insurance ◽  
Monte Carlo Simulation Study ◽  
Heavy Tailed ◽  
Modeling Data ◽  
Insurance Data

Heavy-tailed distributions play an important role in modeling data in actuarial and financial sciences. In this article, a new method is suggested to define new distributions suitable for modeling data with a heavy right tail. The proposed method may be named as the Z-family of distributions. For illustrative purposes, a special submodel of the proposed family, called the Z-Weibull distribution, is considered in detail to model data with a heavy right tail. The method of maximum likelihood estimation is adopted to estimate the model parameters. A brief Monte Carlo simulation study for evaluating the maximum likelihood estimators is done. Furthermore, some actuarial measures such as value at risk and tail value at risk are calculated. A simulation study based on these actuarial measures is also done. An application of the Z-Weibull model to the earthquake insurance data is presented. Based on the analyses, we observed that the proposed distribution can be used quite effectively in modeling heavy-tailed data in insurance sciences and other related fields. Finally, Bayesian analysis and performance of Gibbs sampling for the earthquake data have also been carried out.

scholarly journals Marshall–Olkin Alpha Power Weibull Distribution: Different Methods of Estimation Based on Type-I and Type-II Censoring

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Ehab M. Almetwally ◽  
Mohamed A. H. Sabry ◽  
Randa Alharbi ◽  
Dalia Alnagar ◽  
Sh. A. M. Mubarak ◽  
...  
Keyword(s):  
Weibull Distribution ◽  
Likelihood Estimation ◽  
Real Data ◽  
Estimation Methods ◽  
Data Sets ◽  
Type I ◽  
Alpha Power ◽  
Type Ii ◽  
Censored Samples ◽  
Distribution Parameters

This paper introduces the new novel four-parameter Weibull distribution named as the Marshall–Olkin alpha power Weibull (MOAPW) distribution. Some statistical properties of the distribution are examined. Based on Type-I censored and Type-II censored samples, maximum likelihood estimation (MLE), maximum product spacing (MPS), and Bayesian estimation for the MOAPW distribution parameters are discussed. Numerical analysis using real data sets and Monte Carlo simulation are accomplished to compare various estimation methods. This novel model’s supremacy upon some famous distributions is explained using two real data sets and it is shown that the MOAPW model can achieve better fits than other competitive distributions.

scholarly journals Marshall–Olkin Alpha Power Lomax Distribution: Estimation Methods, Applications on Physics and Economics

2021 ◽  
pp. 137-153
Author(s):  
Hisham Mohamed Almongy ◽  
Ehab Mohamed Almetwally ◽  
Amaal Elsayed Mubarak
Keyword(s):  
Monte Carlo Simulation ◽  
Numerical Study ◽  
Likelihood Estimation ◽  
Real Data ◽  
Least Square ◽  
Estimation Methods ◽  
Data Sets ◽  
Alpha Power ◽  
Lomax Distribution ◽  
Distribution Parameters

In this paper, we introduce and study a new extension of Lomax distribution with four-parameter named as the Marshall–Olkin alpha power Lomax (MOAPL) distribution. Some statistical properties of this distribution are discussed. Maximum likelihood estimation (MLE), maximum product spacing (MPS) and least Square (LS) method for the MOAPL distribution parameters are discussed. A numerical study using real data analysis and Monte-Carlo simulation are performed to compare between different methods of estimation. Superiority of the new model over some well-known distributions are illustrated by physics and economics real data sets. The MOAPL model can produce better fits than some well-known distributions as Marshall–Olkin Lomax, alpha power Lomax, Lomax distribution, Marshall–Olkin alpha power exponential, Kumaraswamy-generalized Lomax, exponentiated  Lomax  and power Lomax.

Sign in / Sign up

Export Citation Format

Share Document