scholarly journals A New Exponential-X Family: Modeling Extreme Value Data in the Finance Sector

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Zubair Ahmad ◽  
Eisa Mahmoudi ◽  
Rasool Roozegar ◽  
Morad Alizadeh ◽  
Ahmed Z. Afify
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Statistical Models ◽  
Claims Data ◽  
Maximum Likelihood Estimators ◽  
Weibull Model ◽  
Insurance Claims Data ◽  
Practical Analysis ◽  
Heavy Tailed ◽  
Modeling Data

In this paper, a family of statistical models, namely, a new exponential-X family is proposed. A subcase of the introduced family, called the new exponential-Weibull (NE-Weibull) model, is studied. The NE-Weibull model is very competent and possesses heavy-tailed properties. The maximum likelihood estimators of its parameters are derived. The consistency and efficiency of these estimators are assessed in a brief simulation study. Finally, the effectiveness of the NE-Weibull distribution is illustrated by modeling real insurance claims data. The practical analysis shows that the NE-Weibull distribution outclassed other distributions and it can be a better choice for modeling data in the finance sector.

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 Statistical Inference for the Weibull Distribution Based on δ-Record Data

Symmetry ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 20 ◽  
Author(s):  
Raúl Gouet ◽  
F. Javier López ◽  
Lina Maldonado ◽  
Gerardo Sanz
Keyword(s):  
Maximum Likelihood ◽  
Experimental Design ◽  
Weibull Distribution ◽  
Bayesian Estimation ◽  
Statistical Inference ◽  
Numerical Computation ◽  
Weibull Model ◽  
Rainfall Series ◽  
Estimation Of Parameters ◽  
Record Data

We consider the maximum likelihood and Bayesian estimation of parameters and prediction of future records of the Weibull distribution from δ -record data, which consists of records and near-records. We discuss existence, consistency and numerical computation of estimators and predictors. The performance of the proposed methodology is assessed by Montecarlo simulations and the analysis of monthly rainfall series. Our conclusion is that inferences for the Weibull model, based on δ -record data, clearly improve inferences based solely on records. This methodology can be recommended, more so as near-records can be collected along with records, keeping essentially the same experimental design.

Estimation of Weibull Parameters Using Fractional Moments

1984 ◽  
Vol 33 (3-4) ◽  
pp. 179-186 ◽  
Author(s):  
S.P. Mukherjee ◽  
B.C. Sasmal
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Relative Efficiency ◽  
Maximum Likelihood Estimators ◽  
Weibull Parameters ◽  
Moment Estimators ◽  
Fractional Moments ◽  
Distribution Moment ◽  
The Moment ◽  
Two Parameter

For a two-parameter Weibull distribution, moment estimators of the parameters have been developed by choosing orders of two moments (allowing fractions) so that the overall relative efficiency of the moment estimators compared with the maximum likelihood estimators is maximized . Some calculations in support of the superiority of fractional moments over integer moments in this connection have also been presented.

Finding maximum likelihood estimators for the three-parameter Weibull distribution

1994 ◽  
Vol 5 (4) ◽  
pp. 373-397 ◽  
Author(s):  
�ric Gourdin ◽  
Pierre Hansen ◽  
Brigitte Jaumard
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Maximum Likelihood Estimators

scholarly journals A New Flexible Family of Continuous Distributions: The Additive Odd-G Family

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1837
Author(s):  
Emrah Altun ◽  
Mustafa Ç. Korkmaz ◽  
Mahmoud El-Morshedy ◽  
Mohamed S. Eliwa
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Additive Model ◽  
Maximum Likelihood Estimators ◽  
Model Parameters ◽  
Model Structure ◽  
Simulation Studies ◽  
New Family ◽  
Family Based ◽  
Family Of Distributions

This paper introduces a new family of distributions based on the additive model structure. Three submodels of the proposed family are studied in detail. Two simulation studies were performed to discuss the maximum likelihood estimators of the model parameters. The log location-scale regression model based on a new generalization of the Weibull distribution is introduced. Three datasets were used to show the importance of the proposed family. Based on the empirical results, we concluded that the proposed family is quite competitive compared to other models.

scholarly journals Bias-Corrected Maximum Likelihood Estimators of the Parameters of the Unit-Weibull Distribution

2021 ◽  
Vol 50 (3) ◽  
pp. 41-53
Author(s):  
Andre Menezes ◽  
Josmar Mazucheli ◽  
F. Alqallaf ◽  
M. E. Ghitany
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Parametric Bootstrap ◽  
Real Data ◽  
Bias Reduction ◽  
Maximum Likelihood Estimates ◽  
Data Sets ◽  
Analytical Methodology ◽  
Finite Samples ◽  
Modeling Data

It is well known that the maximum likelihood estimates (MLEs) have appealing statistical properties. Under fairly mild conditions their asymptotic distribution is normal, and no other estimator has a smaller asymptotic variance.However, in finite samples the maximum likelihood estimates are often biased estimates and the bias disappears as the sample size grows.Mazucheli, Menezes, and Ghitany (2018b) introduced a two-parameter unit-Weibull distribution which is useful for modeling data on the unit interval, however its MLEs are biased in finite samples.In this paper, we adopt three approaches for bias reduction of the MLEs of the parameters of unit-Weibull distribution.The first approach is the analytical methodology suggested by Cox and Snell (1968), the second is based on parametric bootstrap resampling method, and the third is the preventive approach introduced by Firth (1993).The results from Monte Carlo simulations revealed that the biases of the estimates should not be ignored and the bias reduction approaches are equally efficient. However, the first approach is easier to implement.Finally, applications to two real data sets are presented for illustrative purposes.

scholarly journals The Arctan-X Family of Distributions: Properties, Simulation, and Applications to Actuarial Sciences

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Ibrahim Alkhairy ◽  
M. Nagy ◽  
Abdisalam Hassan Muse ◽  
Eslam Hussam
Keyword(s):  
Weibull Distribution ◽  
Model Comparison ◽  
Simulation Analysis ◽  
Likelihood Estimation ◽  
Weibull Model ◽  
Trigonometric Function ◽  
Data Sets ◽  
Data Set ◽  
Heavy Tailed ◽  
Family Of Distributions

The purpose of this paper is to investigate a new family of distributions based on an inverse trigonometric function known as the arctangent function. In the context of actuarial science, heavy-tailed probability distributions are immensely beneficial and play an important role in modelling data sets. Actuaries are committed to finding for such distributions in order to get an excellent fit to complex economic and actuarial data sets. The current research takes a look at a popular method for generating new distributions which are excellent candidates for dealing with heavy-tailed data. The proposed family of distributions is known as the Arctan-X family of distributions and is introduced using an inverse trigonometric function. For the specific purpose of the show of strength, we studied the Arctan-Weibull distribution as a special case of the developed family. To estimate the parameters of the Arctan-Weibull distribution, the frequentist approach, i.e., maximum likelihood estimation, is used. A rigorous Monte Carlo simulation analysis is used to determine the efficiency of the obtained estimators. The Arctan-Weibull model is demonstrated using a real-world insurance data set. The Arctan-Weibull is compared to well-known two-, three-, and four-parameter competitors. Among the competing distributions are Weibull, Kappa, Burr-XII, and beta-Weibull. For model comparison, we used the most precise tests used to know whether the Arctan-Weibull distribution is more useful than competing models.

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