scholarly journals The Truncated Burr X-G Family of Distributions: Properties and Applications to Actuarial and Financial Data

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 1088
Author(s):  
Rashad A. R. Bantan ◽  
Christophe Chesneau ◽  
Farrukh Jamal ◽  
Ibrahim Elbatal ◽  
Mohammed Elgarhy
Keyword(s):  
Risk Measures ◽  
Financial Data ◽  
Model Parameters ◽  
Nested Models ◽  
Continuous Type ◽  
Order Stochastic Dominance ◽  
New Family ◽  
Peak Asymmetry ◽  
Rate Functions ◽  
Special Distribution

In this article, the “truncated-composed” scheme was applied to the Burr X distribution to motivate a new family of univariate continuous-type distributions, called the truncated Burr X generated family. It is mathematically simple and provides more modeling freedom for any parental distribution. Additional functionality is conferred on the probability density and hazard rate functions, improving their peak, asymmetry, tail, and flatness levels. These characteristics are represented analytically and graphically with three special distributions of the family derived from the exponential, Rayleigh, and Lindley distributions. Subsequently, we conducted asymptotic, first-order stochastic dominance, series expansion, Tsallis entropy, and moment studies. Useful risk measures were also investigated. The remainder of the study was devoted to the statistical use of the associated models. In particular, we developed an adapted maximum likelihood methodology aiming to efficiently estimate the model parameters. The special distribution extending the exponential distribution was applied as a statistical model to fit two sets of actuarial and financial data. It performed better than a wide variety of selected competing non-nested models. Numerical applications for risk measures are also given.

scholarly journals The Transmuted Odd Fréchet-G Family of Distributions: Theory and Applications

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 958 ◽  
Author(s):  
Majdah M. Badr ◽  
Ibrahim Elbatal ◽  
Farrukh Jamal ◽  
Christophe Chesneau ◽  
Mohammed Elgarhy
Keyword(s):  
Cumulative Distribution Function ◽  
Parametric Estimation ◽  
Cumulative Distribution ◽  
Data Sets ◽  
Additional Parameter ◽  
New Family ◽  
Rate Functions ◽  
Special Distribution ◽  
Standard Exponential Distribution ◽  
Modeling Strategy

The last years, the odd Fréchet-G family has been considered with success in various statistical applications. This notoriety can be explained by its simple and flexible exponential-odd structure quite different to the other existing families, with the use of only one additional parameter. In counter part, some of its statistical properties suffer of a lack of adaptivity in the sense that they really depend on the choice of the baseline distribution. Hence, efforts have been made to relax this subjectivity by investigating extensions or generalizations of the odd transformation at the heart of the construction of this family, with the aim to reach new perspectives of applications as well. This study explores another possibility, based on the transformation of the whole cumulative distribution function of this family (while keeping the odd transformation intact), through the use of the quadratic rank transmutation that has proven itself in other contexts. We thus introduce and study a new family of flexible distributions called the transmuted odd Fréchet-G family. We show how the former odd Fréchet-G family is enriched by the proposed transformation through theoretical and practical results. We emphasize the special distribution based on the standard exponential distribution because of its desirable features for the statistical modeling. In particular, different kinds of monotonic and nonmonotonic shapes for the probability density and hazard rate functions are observed. Then, we show how the new family can be used in practice. We discuss in detail the parametric estimation of a special model, along with a simulation study. Practical data sets are handle with quite favorable results for the new modeling strategy.

scholarly journals The Topp-Leone Marshall-Olkin-G Family of Distributions With Applications

2020 ◽  
Vol 9 (4) ◽  
pp. 15
Author(s):  
Fastel Chipepa ◽  
Broderick Oluyede ◽  
Boikanyo Makubate
Keyword(s):  
Linear Combination ◽  
Simulation Study ◽  
Hazard Rate ◽  
Model Parameters ◽  
Nested Models ◽  
Rate Functions ◽  
Heavy Tailed ◽  
New Distribution ◽  
Generalized Distribution ◽  
Family Of Distributions

A new generalized distribution is developed, namely, Topp-Leone Marshall-Olkin-G distribution. The new distribution is a linear combination of the exponentiated-G family of distributions. We considered three sub-families of the new proposed family of distribution. The distribution can handle heavy-tailed data and various forms of the hazard rate functions. A simulation study was conducted to evaluate consistency of the model parameters. Three applications are provided to demonstrate the usefulness of the new model in comparison with competing non-nested models.

scholarly journals Multivariate extensions of expectiles risk measures

2017 ◽  
Vol 5 (1) ◽  
pp. 20-44 ◽  
Author(s):  
Véronique Maume-Deschamps ◽  
Didier Rullière ◽  
Khalil Said
Keyword(s):  
Stochastic Approximation ◽  
Risk Measures ◽  
New Family ◽  
Vector Valued

Abstract This paper is devoted to the introduction and study of a new family of multivariate elicitable risk measures. We call the obtained vector-valued measures multivariate expectiles. We present the different approaches used to construct our measures. We discuss the coherence properties of these multivariate expectiles. Furthermore, we propose a stochastic approximation tool of these risk measures.

scholarly journals The extended odd family of probability distributions with practice to a submodel

Filomat ◽  
2019 ◽  
Vol 33 (12) ◽  
pp. 3855-3867 ◽  
Author(s):  
Hassan Bakouch ◽  
Christophe Chesneau ◽  
Muhammad Khan
Keyword(s):  
Heavy Tails ◽  
Maximum Likelihood Method ◽  
Probability Distributions ◽  
Likelihood Method ◽  
Tuning Parameter ◽  
Data Sets ◽  
New Family ◽  
Rate Functions ◽  
Special Case ◽  
Family Of Distributions

In this paper, we introduce a new family of distributions extending the odd family of distributions. A new tuning parameter is introduced, with some connections to the well-known transmuted transformation. Some mathematical results are obtained, including moments, generating function and order statistics. Then, we study a special case dealing with the standard loglogistic distribution and the modifiedWeibull distribution. Its main features are to have densities with flexible shapes where skewness, kurtosis, heavy tails and modality can be observed, and increasing-decreasing-increasing, unimodal and bathtub shaped hazard rate functions. Estimation of the related parameters is investigated by the maximum likelihood method. We illustrate the usefulness of our extended odd family of distributions with applications to two practical data sets.

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 Extended Odd Fréchet-G Family of Distributions

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Suleman Nasiru
Keyword(s):  
Maximum Likelihood Method ◽  
Real Data ◽  
Likelihood Method ◽  
Data Sets ◽  
Data Set ◽  
New Class ◽  
New Family ◽  
Rate Functions ◽  
The Given ◽  
Family Of Distributions

The need to develop generalizations of existing statistical distributions to make them more flexible in modeling real data sets is vital in parametric statistical modeling and inference. Thus, this study develops a new class of distributions called the extended odd Fréchet family of distributions for modifying existing standard distributions. Two special models named the extended odd Fréchet Nadarajah-Haghighi and extended odd Fréchet Weibull distributions are proposed using the developed family. The densities and the hazard rate functions of the two special distributions exhibit different kinds of monotonic and nonmonotonic shapes. The maximum likelihood method is used to develop estimators for the parameters of the new class of distributions. The application of the special distributions is illustrated by means of a real data set. The results revealed that the special distributions developed from the new family can provide reasonable parametric fit to the given data set compared to other existing distributions.

scholarly journals A New Extended Two-Parameter Distribution: Properties, Estimation Methods, and Applications in Medicine and Geology

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1578 ◽  
Author(s):  
Hazem Al-Mofleh ◽  
Ahmed Z. Afify ◽  
Noor Akma Ibrahim
Keyword(s):  
Estimation Method ◽  
Estimation Methods ◽  
Parameter Distribution ◽  
Model Parameters ◽  
Unknown Parameters ◽  
Proposed Model ◽  
Rate Functions ◽  
The Mean ◽  
Modeling Data ◽  
Two Parameter

In this paper, a new two-parameter generalized Ramos–Louzada distribution is proposed. The proposed model provides more flexibility in modeling data with increasing, decreasing, J-shaped, and reversed-J shaped hazard rate functions. Several statistical properties of the model were derived. The unknown parameters of the new distribution were explored using eight frequentist estimation approaches. These approaches are important for developing guidelines to choose the best method of estimation for the model parameters, which would be of great interest to practitioners and applied statisticians. Detailed numerical simulations are presented to examine the bias and the mean square error of the proposed estimators. The best estimation method and ordering performance of the estimators were determined using the partial and overall ranks of all estimation methods for various parameter combinations. The performance of the proposed distribution is illustrated using two real datasets from the fields of medicine and geology, and both datasets show that the new model is more appropriate as compared to the Marshall–Olkin exponential, exponentiated exponential, beta exponential, gamma, Poisson–Lomax, Lindley geometric, generalized Lindley, and Lindley distributions, among others.

Stable Stationary Solitons of the One-Dimensional Modified Complex Ginzburg-Landau Equation

2007 ◽  
Vol 62 (7-8) ◽  
pp. 368-372
Author(s):  
Woo-Pyo Hong
Keyword(s):  
Landau Equation ◽  
Model Parameters ◽  
Ginzburg Landau ◽  
One Dimensional ◽  
Paraxial Ray Approximation ◽  
New Family ◽  
Ginzburg Landau Equation ◽  
The Stability ◽  
The One ◽  
Paraxial Ray

We report on the existence of a new family of stable stationary solitons of the one-dimensional modified complex Ginzburg-Landau equation. By applying the paraxial ray approximation, we obtain the relation between the width and the peak amplitude of the stationary soliton in terms of the model parameters. We verify the analytical results by direct numerical simulations and show the stability of the stationary solitons.

scholarly journals An Inverse Gamma Activity Time Process with Noninteger Parameters and a Self-Similar Limit

2012 ◽  
Vol 49 (02) ◽  
pp. 441-450 ◽  
Author(s):  
Richard Finlay ◽  
Eugene Seneta ◽  
Dingcheng Wang
Keyword(s):  
Long Range ◽  
Financial Data ◽  
Gamma Activity ◽  
Model Parameters ◽  
Model Estimation ◽  
Time Process ◽  
Activity Time ◽  
Inverse Gamma ◽  
Self Similar

We construct a process with inverse gamma increments and an asymptotically self-similar limit. This construction supports the use of long-range-dependent t subordinator models for actual financial data as advocated in Heyde and Leonenko (2005), in that it allows for noninteger-valued model parameters, as is found empirically in model estimation from data.

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