Eisa Mahmoudi
@yazd.ac.ir
Statistics
Faculty Member, Yazd University, Iran
I am a Professor of Statistics and a faculty member for 16 years. Skilled in statistical techniques, data analysis, statistical modelling, statistical inference, survey methodology, actuarial science, financial mathematics and data science. Teaching various graduate and undergraduate courses in statistics and mathematics at the university level, and having experience in analyzing various data by statistical software, especially using R programming. Supervised/co-supervised 7 PhDs and 45 MSc students in various fields of statistics including, Mathematical Statistics, Reliability
Analysis, Sequential Analysis, Financial Mathematics and Actuarial Science.
EDUCATION
SEP 2001 - JUN 2006 Ph.D. Department of Statistics, Shiraz University, Iran, Dissertation: Sequential Point Estimation in a Scale Family of Distributions
SEP 1999 - AUG 2001 M.Sc. Department of Statistics, Shiraz University, Iran Dissertation: A Survey on Bayesian Convolution for Estimation
SEP 1995 - JUNE 1999 B.Sc. Department of Statistics, Shiraz University, Iran
RESEARCH INTERESTS
Financial Mathematics
Data Science
Actuarial Science
Sequential Estimation
Bayesian Inference
Distribution Theory
Scopus Publications
Scholar Citations
Scholar h-index
Scholar i10-index
Scopus Publications
Eisa Mahmoudi, Zahra Nemati, and Ashkan Khalifeh
Informa UK Limited
Abstract We consider the problem of bounded risk point estimation for the linear combination of the form where and are the location and scale parameters of a exponential distribution and and are constant. We aim to estimate under the modified squared error loss function using the constraint that the risk per unit cost is bounded above with fixed preassigned, . The two-stage sequential sampling is proposed for estimating The performances of the proposed methodologies are investigated with the help of simulations. Finally, using an actual dataset, the procedure is clearly illustrated.
Eisa Mahmoudi, Rahmat Sadat Meshkat, and Hamzeh Torabi
Institute of Electrical and Electronics Engineers (IEEE)
In this article, we consider a weighted-<inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula>-out-of-<inline-formula><tex-math notation="LaTeX">$n$</tex-math></inline-formula> system having <inline-formula><tex-math notation="LaTeX">$m \\geq 2$</tex-math></inline-formula> type of components each with its own positive integer-valued weight, in which the random lifetimes of components are dependent. This system is supposed to work with performance level <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula> if and only if the total weight of functioning components of all types is at least <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula>. The structure of dependence of the system component lifetimes is modeled by the copula function. Also, it is assumed that the random numbers <inline-formula><tex-math notation="LaTeX">$N_i$</tex-math></inline-formula> of components are chosen from class <inline-formula><tex-math notation="LaTeX">$D_i$</tex-math></inline-formula> for type <inline-formula><tex-math notation="LaTeX">$i$</tex-math></inline-formula>. The reliability of the system is obtained as a mixture of the reliability of weighted-<inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula>-out-of-<inline-formula><tex-math notation="LaTeX">$n$</tex-math></inline-formula> systems consisting of <inline-formula><tex-math notation="LaTeX">$m$</tex-math></inline-formula> types of components with fixed number of them in terms of the probability mass function of the random vector <inline-formula><tex-math notation="LaTeX">$(N_1, \\ldots,N_{m-1})$</tex-math></inline-formula>. Then, a copula-based expression for component importance in each class is obtained, and illustrative examples are presented.
Rasool Roozegar, Saralees Nadarajah, and Eisa Mahmoudi
Springer Science and Business Media LLC
Eisa Mahmoudi, Zahra Nemati, and Ashkan Khalifeh
Informa UK Limited
Zubair Ahmad, Eisa Mahmoudi, Rasool Roozegarz, G.G. Hamedani, and Nadeem Shafique Butt
Pakistan Journal of Statistics and Operation Research
In the past couple of years, statistical models have been extensively used in applied areas for analyzing real data sets. However, in numerous situations, the traditional distributions are not flexible enough to cater to different aspects of the real phenomena. For example, (i) in the practice of reliability engineering and biomedical analysis, some distributions provide the best fit to the data having monotonic failure rate function, but fails to provide the best fit to the data having non-monotonic failure rate function, (ii) some statistical distributions provide the best fit for small insurance losses, but fails to provide an adequate fit to large claim size data, and (iii) some distributions do not have closed forms causing difficulties in the estimation process. To address the above issues, therefore, several methods have been suggested to improve the flexibility of the classical distributions. In this article, we investigate some of the former methods of generalizing the existing distributions. Further, we propose nineteen new methods of extending the classical distributions to obtain flexible models suitable for modeling data in applied fields. We also provide certain characterizations of the newly proposed families. Finally, we provide a comparative study of the newly proposed and some other existing well-known models via analyzing three real data sets from three different disciplines such as reliability engineering, medical, and financial sciences.
Zubair Ahmad, Eisa Mahmoudi, and Gholamhossien Hamedani
Informa UK Limited
Abstract Actuaries are often in search of finding an adequate model for actuarial and financial risk management problems. In the present work, we introduce a class of claim distributions useful in a number of lifetime analyses. A special sub-model of the proposed family, called the Weibull claim model, is considered in detail. Some mathematical properties along with certain characterizations are derived and maximum likelihood estimates of the model parameters are obtained. A simulation study has been carried out to evaluate the performance of the maximum likelihood estimators. Furthermore, some actuarial measures such as value at risk, tail value at risk, tail variance and tail premium variance are calculated. A simulation study based on these actuarial measures is done. Finally, two applications of the proposed model to the insurance claim data set are presented.
Zubair Ahmad, Eisa Mahmoudi, and Sanku Dey
Informa UK Limited
Heavy tailed distributions play very significant role in the study of actuarial and financial risk management data but the probability distributions proposed to model such data are scanty. Actuarie...
Soudabe Sajjadipanah, Eisa Mahmoudi, and Mohammadsadegh Zamani
Informa UK Limited
A two-stage procedure in a first-order autoregressive model ðARð1ÞÞ is considered that investigates the point and the interval estimation of parameters based on the least squares estimator. The two-stage procedure is shown to be as effective as the best fixed-sample-size procedure. In this regard, the significant properties of the procedure, such as asymptotic risk efficiency, asymptotic efficiency, and asymptotic consistency, are established. A Monte Carlo simulation study is conducted to compare the performance of the two-stage procedure and the purely sequential procedure. Finally, real-time series data are considered to illustrate the applicability of the two-stage procedure. ARTICLE HISTORY Received 6 May 2020 Revised 14 June 2021 Accepted 5 September 2021
Zubair Ahmad, Eisa Mahmoudi, Rasool Roozegar, Morad Alizadeh, and Ahmed Z. Afify
Hindawi Limited
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.
Yen Liang Tung, Zubair Ahmad, and Eisa Mahmoudi
Computers, Materials and Continua (Tech Science Press)
Zubair Ahmad, Eisa Mahmoudi, Morad Alizadeh, Rasool Roozegar, and Ahmed Z. Afify
Hindawi Limited
Heavy-tailed distributions play a prominent role in actuarial and financial sciences. In this paper, we introduce a family of distributions that we refer to as exponential T-X (ETX) family. Based on the proposed approach, a new extension of the Weibull model is introduced. The proposed model is very flexible in modeling heavy-tailed data. Some mathematical properties are derived, and maximum likelihood estimates of the model parameters are obtained. A Monte Carlo simulation study is conducted to evaluate the performance of the maximum likelihood estimators. Actuarial measures such as value at risk and tail value at risk are also calculated. A simulation study based on these actuarial measures is provided. Finally, an application to a heavy-tailed automobile insurance claim data set is presented. The proposed model is compared with some well-known competing distributions.
Jin Zhao, Zubair Ahmad, Eisa Mahmoudi, E. H. Hafez, and Marwa M. Mohie El-Din
Hindawi Limited
Statistical distributions play a prominent role for modeling data in applied fields, particularly in actuarial, financial sciences, and risk management fields. Among the statistical distributions, the heavy-tailed distributions have proven the best choice to use for modeling heavy-tailed financial data. The actuaries are often in search of such types of distributions to provide the best description of the actuarial and financial data. This study presents a new power transformation to introduce a new family of heavy-tailed distributions useful for modeling heavy-tailed financial data. A submodel, namely, heavy-tailed beta-power transformed Weibull model is considered to demonstrate the adequacy of the proposed method. Some actuarial measures such as value at risk, tail value at risk, tail variance, and tail variance premium are calculated. A brief simulation study based on these measures is provided. Finally, an application to the insurance loss dataset is analyzed, which revealed that the proposed distribution is a superior model among the competitors and could potentially be very adequate in describing and modeling actuarial and financial data.
Zubair Ahmad, Eisa Mahmoudi, and G.G. Hamedani
Communications for Statistical Applications and Methods
Heavy tailed distributions are useful for modeling actuarial and financial risk management problems. Actuaries often search for finding distributions that provide the best fit to heavy tailed data sets. In the present work, we introduce a new class of heavy tailed distributions of a special sub-model of the proposed family, called a new extended alpha power transformed Weibull distribution, useful for modeling heavy tailed data sets. Mathematical properties along with certain characterizations of the proposed distribution are presented. Maximum likelihood estimates of the model parameters are obtained. A simulation study is provided to evaluate the performance of the maximum likelihood estimators. Actuarial measures such as Value at Risk and Tail Value at Risk are also calculated. Further, a simulation study based on the actuarial measures is done. Finally, an application of the proposed model to a heavy tailed data set is presented. The proposed distribution is compared with some well-known (i) two-parameter models, (ii) three-parameter models and (iii) four-parameter models.
Ashkan Khalifeh, Eisa Mahmoudi, and Ajit Chaturvedi
Springer Science and Business Media LLC
Eisa Mahmoudi and Ameneh Rostami
Springer Science and Business Media LLC
In this paper, we introduce a first-order nonnegative integer-valuedmoving average process with power series innovations based on a Poisson thinning operator (PINMAPS(1)) formodeling overdispersed, equidispersed and underdispersed count time series. This process contains the PINMA process with geometric, Bernoulli, Poisson, binomial, negative binomial and logarithmic innovations which some of them are studied in details. Some statistical properties of the process are obtained. The unknown parameters of the model are estimated using the Yule-Walker, conditional least squares and least squares feasible generalized methods. Also, the performance of estimators is evaluated using a simulation study. Finally, we apply the model to three real data set and show the ability of the model for predicting data compared to competing models.
Eisa Mahmoudi and RahmatSadat Meshkat
Springer Science and Business Media LLC
This paper introduces a special case of weightedk-out-ofn:G system formed from two types of nonidentical components with different weights. This system consists of n nonidentical components each with its own positive integer-valued weight which are categorized into two groups with respect to their duties and services. In fact, we have a system consisting n components such that n1 of them each with its own weight ωi and reliability p1i and n2 of them each with its own weight ω∗ i and reliability p2i. If the total weights of the functioning components exceeds a prespecified threshold k, the system is supposed to work. The reliability of system is obtained based on the total weight of all working components in both group. The survival function and mean time to failure are presented. Also, the component importance of this system are studied.
Zubair Ahmad, Eisa Mahmoudi, Sanku Dey, and Saima K. Khosa
Springer Science and Business Media LLC
In actuarial literature, we come across a diverse range of probability distributions for fitting insurance loss data. Popular distributions are lognormal, log-t, various versions of Pareto, log-logistic, Weibull, gamma and its variants and a generalized beta of the second kind, among others. In this paper, we try to supplement the distribution theory literature by incorporating the heavy tailed model, called weighted T-X Weibull distribution. The proposed distribution exhibits desirable properties relevant to the actuarial science and inference. Shapes of the density function and key distributional properties of the weighted T-X Weibull distribution are presented. Some actuarial measures such as value at risk, tail value at risk, tail variance and tail variance premium are calculated. A simulation study based on the actuarial measures is provided. Finally, the proposed method is illustrated via analyzing vehicle insurance loss data.
Ashkan Khalifeh, Eisa Mahmoudi, Ali Dolati, , , and
CMV Verlag
In this paper, two-stage and purely sequential estimation procedures are considered to construct fixed-width confidence intervals for the reliability parameter under the stress-strength model when the stress and strength are independent exponential random variables with different scale parameters. The exact distribution of the stopping rule under the purely sequential procedure is approximated using the law of large numbers and Monte Carlo integration. For the two-stage sequential procedure, explicit formulas for the distribution of the total sample size, the expected value and mean squared error of the maximum likelihood estimator of the reliability parameter under the stress-strength model are provided. Moreover, it is shown that both proposed sequential procedures are finite, and in exceptional cases, the exact distribution of stopping times is degenerate distribution at the initial sample size. The performances of the proposed methodologies are investigated with the help of simulations. Finally using real data, the procedures are clearly illustrated.
Zubair Ahmad, Eisa Mahmoudi, and Morad Alizadeh
Informa UK Limited
Abstract Actuaries are often in search of new distributions suitable for modeling financial and insurance losses. In this work, we propose a new family of distributions, called a new beta power transformed family of distributions. A special sub-model of the proposed class, called a new beta power transformed Weibull, suitable for modeling heavy tailed data in the scenario of actuarial statistics and finance, is considered in detail. The proposed distribution possesses desirable properties relevant to actuarial sciences. Expressions for the actuarial quantities such as value at risk, tail value at risk, tailed variance and tailed variance premium are derived. A simulation study is conducted to evaluate the behavior of the proposed distribution in actuarial sciences. Some distributional properties with estimation of parameters using maximum likelihood method are also discussed. Finally, a practical application of the proposed model to insurance data is presented.
Zubair Ahmad, Eisa Mahmoudi, and Omid Kharazmi
Hindawi Limited
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.
Qinghu Liao, Zubair Ahmad, Eisa Mahmoudi, and G. G. Hamedani
Hindawi Limited
Many studies have suggested the modifications and generalizations of the Weibull distribution to model the nonmonotone hazards. In this paper, we combine the logarithms of two cumulative hazard rate functions and propose a new modified form of the Weibull distribution. The newly proposed distribution may be called a new flexible extended Weibull distribution. Corresponding hazard rate function of the proposed distribution shows flexible (monotone and nonmonotone) shapes. Three different characterizations along with some mathematical properties are provided. We also consider the maximum likelihood estimation procedure to estimate the model parameters. For the illustrative purposes, two real applications from reliability engineering with bathtub-shaped hazard functions are analyzed. The practical applications show that the proposed model provides better fits than the other nonnested models.
Zubair Ahmad, Eisa Mahmoudi, G. G. Hamedani, and Omid Kharazmi
Informa UK Limited
Heavy-tailed distributions play an important role in modelling data in actuarial and financial sciences. In this article, nine new methods are suggested to define new distributions suitable for modelling data with an heavy right tail. For illustrative purposes, a special sub-model is considered in detail. Maximum likelihood estimators of the model parameters are obtained and a Monte Carlo simulation study is carried out to assess the behaviour of the estimators. Furthermore, some actuarial measures are calculated. A simulation study based on these actuarial measures is done. The usefulness of the proposed model is proved empirically by means of two real data sets. Finally, Bayesian analysis and performance of Gibbs sampling for the data sets are also carried out.
Yinglin Liu, Muhammad Ilyas, Saima K. Khosa, Eisa Muhmoudi, Zubair Ahmad, Dost Muhammad Khan, and G. G Hamedani
Hindawi Limited
Statistical distributions play a prominent role in applied sciences, particularly in biomedical sciences. The medical data sets are generally skewed to the right, and skewed distributions can be used quite effectively to model such data sets. In the present study, therefore, we propose a new family of distributions to model right skewed medical data sets. The proposed family may be named as a flexible reduced logarithmic-X family. The proposed family can be obtained via reparameterizing the exponentiated Kumaraswamy G-logarithmic family and the alpha logarithmic family of distributions. A special submodel of the proposed family called, a flexible reduced logarithmic-Weibull distribution, is discussed in detail. Some mathematical properties of the proposed family and certain related characterization results are presented. The maximum likelihood estimators of the model parameters are obtained. A brief Monte Carlo simulation study is done to evaluate the performance of these estimators. Finally, for the illustrative purposes, three applications from biomedical sciences are analyzed and the goodness of fit of the proposed distribution is compared to some well-known competitors.
Eisa Mahmoudi, Ghahraman Roughani, and Ashkan Khalifeh
Springer Science and Business Media LLC
We consider the purely sequential procedure for estimating the scale parameter of a gamma distribution with known shape parameter, when the risk function is bounded by the known preassigned number. In this paper, we provide asymptotic formulas for the expectation of the total sample size. Also, we propose how to adjust the stopping variable so that the risk is uniformly bounded by a known preassigned number. In the end, the performances of the proposed methodology are investigated with the help of simulations and also by using a real data set.