eng
Yazd University
Journal of Statistical Modelling: Theory and Applications
2676-7392
2716-9790
2020-01-01
1
1
1
11
10.22034/jsmta.2020.1698
1698
Computational approach test in one-way fixed effects ANOVA models of log-normal samples
Kamel Abdollahnezhad
k.abdollahnezhad@gu.ac.ir
1
Saba Aghadoust
2
Department of Statistics, Golestan University, Gorgan, Iran
Department of Statistics, Golestan University, Gorgan, Iran
We apply a recently developed computational approach test to the one-way fixed effects ANOVA models of log-normal data with unequal variances. The merits of the proposed test are numerically compared with the existing tests - the James second order test, the Welch test and the Alexander-Govern test - with respect to their sizes and powers in different combinations of parameters and various sample sizes. The simulation results demonstrate that the proposed method is satisfactory: its type I error probability is very close to the nominal level. We illustrate these approaches using a real example.
https://jsm.yazd.ac.ir/article_1698_9aa57d69c55d8fc669172a7e1b903e05.pdf
Actual size
Computational Approach Test
Log-normal Distribution
Power
eng
Yazd University
Journal of Statistical Modelling: Theory and Applications
2676-7392
2716-9790
2020-01-01
1
1
13
27
10.22034/jsmta.2020.1706
1706
A new extended alpha power transformed family of distributions: properties and applications
Zubair Ahmad
z.ferry21@gmail.com
1
M. Elgarhy
m_elgarhy85@yahoo.com
2
Nasir Abbas
3
Department of Statistics, Quaid-i-Azam University 45320, Islamabad, Pakistan
Vice Presidency for Graduate Studies and Scientific Research, University of Jeddah, Jeddah, KSA
Department of Statistics, Government Postgraduate College Jhang, Pakistan
In this paper, a new method has been proposed to introduce an extra parameter to a family of lifetime distributions for more flexibility. A special sub-case has been considered in details namely; two parameters Weibull distribution. Various mathematical properties of the proposed distribution, including explicit expressions for the moments, quantile, moment generating function, residual life, mean residual life and order statistics are derived. The maximum likelihood estimators of unknown parameters cannot be obtained in explicit forms, and they have to be obtained by solving non-linear equations only. A simulation study is conducted to evaluate the performances of these estimators. For the illustrative purposes, two data sets havebeen analyzed to show how the proposed model work in practice.
https://jsm.yazd.ac.ir/article_1706_29be316a5dd550e89d97d1245e6c32da.pdf
Alpha power transformation
Family of distributions
Maximum likelihood estimation
Moments
Order statistic
Residual life function
Weibull distribution
eng
Yazd University
Journal of Statistical Modelling: Theory and Applications
2676-7392
2716-9790
2020-01-01
1
1
29
52
10.22034/jsmta.2020.1707
1707
The exponentiated odd log-logistic family of distributions: properties and applications
Morad Alizadeh
moradalizadeh78@gmail.com
1
Saeid Tahmasebi
tahmasebi@pgu.ac.ir
2
Hossein Haghbin
haghbin@pgu.ac.ir
3
Department of Statistics, Persian Gulf University, Bushehr, Iran
Department of Statistics, Persian Gulf University, Bushehr, Iran
Department of Statistics, Persian Gulf University, Bushehr, Iran
Based on the generalized log-logistic family (Gleaton and Lynch (2006)) of distributions, we propose a new family of continuous distributions with two extra shape parameters called the exponentiated odd log-logistic family. It extends the class of exponentiated distributions, odd log-logistic family (Gleaton and Lynch (2006)) and any continuous distribution by adding two shape parameters. Some special cases of this family are discussed. We investigate the shapes of the density and hazard rate functions. The proposed family has also tractable properties such as various explicit expressions for the ordinary and incomplete moments, quantile and generating functions, probability weighted moments, Bonferroni and Lorenz curves, Shannon and Rényi entropies, extreme values and order statistics, which hold for any baseline model. The model parameters are estimated by maximum likelihood and the usefulness of the new family is illustrated by means of three real data sets.
https://jsm.yazd.ac.ir/article_1707_b9670f57c6e5f698bf734b8082cc15b4.pdf
Generated family
Maximum likelihood
Moment
Odd log-logistic distribution
Probability weighted moment
Quantile function
Rényi entropy
eng
Yazd University
Journal of Statistical Modelling: Theory and Applications
2676-7392
2716-9790
2020-01-01
1
1
53
64
10.22034/jsmta.2020.1708
1708
Comparisons for series and parallel systems with discrete Weibull components via separate comparisons of parameters
Ghobad Barmalzan
ghobad.barmalzan@gmail.com
1
Department of Statistics, University of Zabol, Sistan and Baluchestan, Iran
In this paper, we obtain the usual stochastic order of series and parallel systems comprising heterogeneous discrete Weibull (DW) components. Suppose X1,...,Xn and Y1,...,Yn denote the independent component¢s lifetimes of two systems such that Xi ~ DW(bi, p i) and Yi ~ DW(b*i, p *i), i=1,...,n. We obtain the usual stochastic order between series systems when the vector \boldsymbolb is switched to the vector b*with respect to the majorization order, and when the vector log (1-p) is switched to the vector log (1-p *) in the sense of the weak supermajorization order. We also discuss the usual stochastic order between series systems by using the unordered majorization between the vectors log(1-p) and log (1-p *), and the p-majorization order between the parameters \boldsymbolb and b*. It is also shown that the usual stochastic order between parallel systems comprising heterogeneous discrete Weibull components when the vector log p is switched to the vector log p *in the sense of the weak supermajorization order. These results enable us to find some lower bounds for the survival functions of a series and parallel systems consisting of independent heterogeneous discrete Weibull components.
https://jsm.yazd.ac.ir/article_1708_7719c453b27eafaf30da028b9daf03fa.pdf
Discrete Weibull distribution
P-majorization order
Unordered majorization order
Weak submajorization order
Weak supermajorization order
eng
Yazd University
Journal of Statistical Modelling: Theory and Applications
2676-7392
2716-9790
2020-01-01
1
1
65
89
10.22034/jsmta.2020.1904
1904
The odd generalized half-logistic Weibull-G family of distributions: properties and applications
Fastel Chipepa
chipepa.fastel@studentmail.biust.ac.bw
1
Broderick Oluyede
oluyedeo@biust.ac.bw
2
Boikanyo Makubate
makubateb@biust.ac.bw
3
Department of Mathematics and Statistical Sciences, Botswana International University of Science and Technology
Department of Mathematics and Statistical Sciences, BIUST, Palapye, BW
Department of Mathematics and Statistical Sciences, BIUST, Palapye, BW
We propose a new generalized family of distributions called the odd generalized half logistic Weibull-G family of distributions. We also considered some special cases when the baseline distribution are uniform, Weibull and normal distributions. Structural properties of the new family of distributions including expansion of density, distribution of order statistics, Rényi entropy, moments, probability weighted moments, quantile and generating functions, and maximum likelihood estimates were derived. A characterization based on conditional expectation is presented. A simulation study to examine efficiency of the maximum likelihood estimates is also conducted. Finally, a real data example is presented to illustrate the applicability and usefulness of the proposed model.
https://jsm.yazd.ac.ir/article_1904_02d074f75a369a2359f74cc8143642e7.pdf
Half Logistic Distribution
Half Logistic-G Distribution
Weibull-G Distribution
Maximum likelihood estimation
eng
Yazd University
Journal of Statistical Modelling: Theory and Applications
2676-7392
2716-9790
2020-01-01
1
1
91
100
10.22034/jsmta.2020.1710
1710
Mathematics of evidences in dynamic systems with exponential component lifetimes and optimal sample size determination
Majid Hashempour
ma.hashempour@hormozgan.ac.ir
1
Mahdi Doostparast
doustparast@um.ac.ir
2
Department of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran
Department of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran
In this paper, statistical evidences in lifetimes of sequential r-out-of-n systems, which are modelled by the concept of sequential order statistics (SOS), coming from homogeneous exponential populations are considered. Weak and misleading evidences in SOS for hypotheses about the population parameter are derived in explicit expressions and their behaviours with respect to the model parameters are studied in details. Optimal sample sizes given a minimum desired level for the decisive and the correct probabilities are provided. It is shown that the optimal sample size does not depend on some model parameters.
https://jsm.yazd.ac.ir/article_1710_c05a4acb9d2c0630e9cdf7e5104c2d0c.pdf
Exponential model
Hypotheses testing
Likelihood ratio
Sequential order statistics
Strong and weak evidences
eng
Yazd University
Journal of Statistical Modelling: Theory and Applications
2676-7392
2716-9790
2020-01-01
1
1
101
109
10.22034/jsmta.2020.1712
1712
On construction confidence interval for linear combination means of several heterogeneous log-normal distributions
Ahad Malekzadeh
malekzadeh@kntu.ac.ir
1
Department of Mathematics, K.N. Toosi University of Technology, P.O. Box 16315-1618, Tehran, Iran.
We consider the problem of constructing confidence interval for linear combination of the means of several log-normal distributions. We apply the generalized confidence interval (GCI) approach and the method of variance estimate recovery (MOVER) to construct confidence intervals for the linear combination of log-normal means. We then compare the performances of the proposed confidence intervals via a simulation study and a real data example. Simulation results show that our proposed MOVER and GCI confidence intervals can be recommended generally for different sample sizes and different number of groups.
https://jsm.yazd.ac.ir/article_1712_ba3f0315f51f26853c03f4c5cac4bee8.pdf
Coverage probability
Generalized confidence interval
Log-normal distribution
Method of variance estimate recovery
Monte Carlo simulation
eng
Yazd University
Journal of Statistical Modelling: Theory and Applications
2676-7392
2716-9790
2020-01-01
1
1
111
127
10.22034/jsmta.2020.1713
1713
Point prediction for the proportional hazards family based on progressive Type-II censoring with binomial removals
RahmatSadat Meshkat
r.meshkat@gmail.com
1
Naeimeh Dehqani
ndehqani@yahoo.com
2
Department of Statistics, Yazd University, 89175-741, Yazd, Iran
Department of Statistics, Yazd University, 89175-741, Yazd, Iran
In this paper, some different predictors are presented for failure times of units censored in a progressively censored sample from proportional hazard rate models, where the number of units removed at each failure time follows a binomial distribution. The maximum likelihood predictors, best unbiased predictors and conditional median predictors are derived. Also, the Bayesian point predictors are investigated for the failure times of units with the three common loss function. Finally, a numerical example and a Monte Carlo simulation study are carried out to compare all the prediction methods discussed in this paper.
https://jsm.yazd.ac.ir/article_1713_a207a97d9558107d8854b884f69fc859.pdf
Bayesian point predictor
Best unbiased predictor
Binomial removal
Conditional median predictor
Maximum likelihood predictor
Monte Carlo simulation
Progressive Type-II censoring
Proportional hazard rate model
eng
Yazd University
Journal of Statistical Modelling: Theory and Applications
2676-7392
2716-9790
2020-01-01
1
1
129
142
10.22034/jsmta.2020.1714
1714
A new simple and powerful normality test for progressively Type-II censored data
Sayyed Mahmoud Mirjalili
mirjalili8@yahoo.com
1
Hossein Nadeb
honadeb@yahoo.com
2
Department of Statistics, Velayat University, Iranshahr, Iran
Department of Statistics, Yazd University, 89175-741, Yazd, Iran
In this paper, a new goodness-of-fit test for a location-scale family based on progressively Type-II censored order statistics is proposed. Using Monte Carlo simulation studies, the present researchers have observed that the proposed test for normality is consistent and quite powerful in comparison with some existing goodness-of-fit tests based on progressively Type-II censored data. Also, the new test statistic for a realdata set is used and the results show that the new proposed test statistic performs well.
https://jsm.yazd.ac.ir/article_1714_ea8b7e1e1e1f50e7037bb35121a8acf5.pdf
Goodness-of-fit testing
Location-scale family
Monte Carlo simulation
Order statistics
Progressive Type-II censoring
spacings
eng
Yazd University
Journal of Statistical Modelling: Theory and Applications
2676-7392
2716-9790
2020-01-01
1
1
143
153
10.22034/jsmta.2020.1715
1715
Preliminary test estimation in Rayleigh distribution under a squared-log error loss
Mehran Naghizadeh Qomi
m.naghizadeh@umz.ac.ir
1
H. Zareefard
2
Yazd University
Department of Statistics, University of Jahrom, Jahrom, Iran
The problem of pretest estimation in Rayleigh type-II censored data under the squared-log error loss (SLEL) is considered. The risk-unbiased estimator is derived and its risk is computed under the SLEL. The pretest estimator based on a point guess about the parameter of interest is constructed and the bias and risk is computed. A comparison study is performed between the pretest estimator and the risk-unbiased estimator. The optimal level of significance and critical values of pretest is obtained using regret minimax method. A real data set is used for illustrative purposes.
https://jsm.yazd.ac.ir/article_1715_d414da20db37c24bd3440484fb881788.pdf
Censored data
Pretest estimators
Rayleigh distribution
Squared log error loss
eng
Yazd University
Journal of Statistical Modelling: Theory and Applications
2676-7392
2716-9790
2020-01-01
1
1
155
167
10.22034/jsmta.2020.1716
1716
On a measure of dependence and its application to ICA
Jafar Rahmanishamsi
jrahmanishamsi@yahoo.com
1
Ahmad Alikhani-Vafa
2
Management and Planning Organization, Yazd, Iran
Department of Statistics, Yazd University, 89175-741, Yazd, Iran
In this article we study a copula-based measure of dependence constructed based on the concept of average quadrant dependence. The rank-based estimator of this index and its asymptotic normality is investigated. An algorithm for independent component analysis is developed whose contrast function is the proposed dependence coefficient.
https://jsm.yazd.ac.ir/article_1716_6e8cc5bc8de1a1078f26e48ac593342e.pdf
Copula
Dependence measure
Independent component analysis
Test of independence
eng
Yazd University
Journal of Statistical Modelling: Theory and Applications
2676-7392
2716-9790
2020-01-01
1
1
169
177
10.22034/jsmta.2020.1733
1733
Modeling insurance data using generalized gamma regression
Hossein Zamani
zamani.huni@hormozgan.ac.ir
1
Marzieh Shekari
shekarimuni@hormozgan.ac.ir
2
Zohreh Pakdaman
zpakdaman@hormozgan.ac.ir
3
Department of Statistics, University of Hormozgan
Department of Statistics, University of Hormozgan
Department of Statistics, University of Hormozgan
The generalized gamma (GG) is a flexible distribution in statistical literature with the special cases of exponential, gamma, Weibull and lognormal distributions. This paper investigates the GG additive model for modeling hospital claim costs. In comparison to other models, the GG is more flexible and has a better performance in modeling positively skewed data. The proposed model was fitted to the hospital costs data from the nationwide inpatient sample of the health care cost and utilization project, a nationwide survey of hospital costs conducted by the U.S. Agency for healthcare research and quality. The results indicate that the claim cost is affected by the given explanatory variables and based on the AIC and BIC criteria, the GG has a better performance for the given data compared to the alternatives.
https://jsm.yazd.ac.ir/article_1733_99bc9b7e9686814b9729113c2694a44c.pdf
Generalized additive models
Generalized gamma distribution
Insurance