Statistical Research and Training Center - Statistical Centre of Iran
Journal of Statistical Research of Iran JSRI
1735-1294
16
1
2019
9
1
A New Lifetime Distribution: The Beta Modified Weibull Power Series Distribution
1
31
EN
Ehsan
Bahrami
Shahid Beheshti Universiti
Samani
Narges
Yarmoghaddam
Shahid Beheshti University
10.52547/jsri.16.1.1
In this paper, we propose a new parametric distribution which called as the Beta Modified Weibull Power Series (BMWPS) distribution. This distribution is obtained by compounding Beta Modified Weibull (BMW) and power series distributions. BMWPS distribution contains, as special sub-models, such as Beta Modified Weibull Poisson (BMWP) distribution, Beta Modified Weibull Geometric (BMWG) distribution, Beta Modified Weibull Logarithmic (BMWL)
distribution, among others. We obtain closed-form expressions for the cumulative distribution, density, survival function, failure rate function, the r-th raw moment and the moments of order statistics. A full likelihood-based approach that allows yielding maximum likelihood estimates of the BMWPS arameters is used. Finally, application to the Aarset data are given.
Lifetime, Beta Modified Weibull distribution, power series distribution, maximum Likelihood estimation, hazard function, Fisher's information matrix
http://jsri.srtc.ac.ir/article-1-323-en.html
http://jsri.srtc.ac.ir/article-1-323-en.pdf
Statistical Research and Training Center - Statistical Centre of Iran
Journal of Statistical Research of Iran JSRI
1735-1294
16
1
2019
9
1
New Estimators for Weibull Distribution Parameters: Comprehensive Comparative Study for Weibull Distribution
33
57
EN
Sahar
sadani
s.sadani@gu.ac.ir
Kamel
abdollahnezhad
k.abdollahnezhad@gu.ac.ir
mahdi
teimouri
teimouri@aut.ac.ir
Vahid
ranjbar
v.ranjbar@gu.ac.ir
10.52547/jsri.16.1.33
In this paper we focus on two topics. Firstly, we propose $U$-statistics for the Weibull distribution parameters. The consistency and asymptotically normality of the introduced $U$-statistics are proved theoretically and by simulations. Several of methods have been proposed for estimating the parameters of Weibull distribution in the literature. These methods include: the generalized least square type 1, the generalized least square type 2, the $L$-moments, the Logarithmic moments, the maximum likelihood estimation, the method of moments, the percentile method, the weighted least square, and weighted maximum likelihood estimation. Secondly, due to lack of a comprehensive comparison between the Weibull distribution parameters estimators, a comprehensive comparison study is made between our proposed $U$-statistics and above nine estimators. In our knowledge, this work is the most comprehensive comparison study for the estimators for the Weibull distribution. Based on simulations, it turns out that different estimators may appeal for different range of the parameters. So, practitioners are allowed to chose the best estimator that is suggested by the goodness-of-fit criteria.
Generalized least square, $L$-moment, logarithmic moment, maximum likelihood estimator, $U$-statistic, Weibull distribution, weighted least square, weighted maximum likelihood.
http://jsri.srtc.ac.ir/article-1-349-en.html
http://jsri.srtc.ac.ir/article-1-349-en.pdf
Statistical Research and Training Center - Statistical Centre of Iran
Journal of Statistical Research of Iran JSRI
1735-1294
16
1
2019
9
1
Bias-corrected Maximum-Likelihood Estimator for the Parameter of the Logarithmic Series Distribution and its Characterizations
59
72
EN
Mahdi
Rasekhi
rasekhimahdi@gmail.com
Gholamhossein
G. Hamedani
g.hamedani@mu.edu
10.52547/jsri.16.1.59
In this article, we study parameter estimation of the logarithmic series distribution. A well-known method of estimation is the maximum likelihood estimate (MLE) and this method for this distribution resulted in a biased estimator for the small sample size datasets. The goal here is to reduce the bias and root mean square error of MLE of the unknown parameter. Employing the Cox and Snell method, a closed-form expression for the bias-reduction of the maximum likelihood estimator of the parameter is obtained. Moreover, the parametric Bootstrap bias correction of the maximum likelihood estimator is studied. The performance of the proposed estimators is investigated via Monte Carlo simulation studies. The numerical results show that the analytical bias-corrected estimator performs better than bootstrapped-based estimator and MLE for small sample sizes. Also, certain useful characterizations of this distribution are presented. An example via a real dataset is presented for the illustrative purposes.
Cox-Snell bias-correction, Bootstrap bias-correction, Logarithmic series distribution, Maximum likelihood estimator, Monte Carlo simulation.
http://jsri.srtc.ac.ir/article-1-350-en.html
http://jsri.srtc.ac.ir/article-1-350-en.pdf
Statistical Research and Training Center - Statistical Centre of Iran
Journal of Statistical Research of Iran JSRI
1735-1294
16
1
2019
9
1
Comparison of Record Ranked Set Sampling and Ordinary Records in Prediction of Future Record Statistics from an Exponential Distribution
73
99
EN
Ehsan
Golzade Gervi
e_golzade_g@yahoo.com
Parviz
Nasiri
pnasiri45@yahoo.com
Mahdi
Salehi
pnasiri45@yahoo.com
10.52547/jsri.16.1.73
In some situations, considering a suitable sampling scheme, to reduce the cost and increase efficiency is crucial. In this study, based on a record ranked set sampling scheme, the likelihood and Bayesian prediction of upper record values from a future sequence are discussed in the exponential model. To this end, under an upper record ranked set sample (RRSS) as an informative sample, the maximum likelihood as well as the Bayes point predictors for future upper record values under squared error (SE) and linear-exponential (LINEX) loss functions are obtained. Furthermore, based on a RRSS scheme, two Bayesian prediction intervals are presented. Prediction intervals are compared in terms of coverage probability and expected length. The results of the RRSS scheme are compared with the one based on ordinary records. Finally, a real data set concerning the daily heat degree is used to evaluate the theoretical results obtained. The results show that، in most of the situations, the RRSS scheme performs better.
Bayesian prediction, maximum likelihood prediction, record values, record ranked set sampling scheme.
http://jsri.srtc.ac.ir/article-1-351-en.html
http://jsri.srtc.ac.ir/article-1-351-en.pdf
Statistical Research and Training Center - Statistical Centre of Iran
Journal of Statistical Research of Iran JSRI
1735-1294
16
1
2019
9
1
New Results on Stochastic Comparison of Series and Parallel Systems Comprising Heterogeneous Generalized Modified Weibull Components
101
120
EN
Esmaeil
Bashkar
e.bashkar@velayat.ac.ir
10.52547/jsri.16.1.101
In this work, we study various stochastic orderings of the smallest and largest order statistics arising from independent heterogeneous generalized modified Weibull (GMW) random variables. We also conduct stochastic comparison on the extreme order statistics from GMW samples with Archimedean copulas. The results established in this paper strengthen and generalize those known in the Balakrishnan et al. (2018).
Majorization, order statistics, series and parallel systems, stochastic orders, generalized modified Weibull distribution.
http://jsri.srtc.ac.ir/article-1-352-en.html
http://jsri.srtc.ac.ir/article-1-352-en.pdf
Statistical Research and Training Center - Statistical Centre of Iran
Journal of Statistical Research of Iran JSRI
1735-1294
16
1
2019
9
1
Spatial Statistics Analysis to Identify Hot Spots Using Accidental Event Calls Services
121
141
EN
Samira
Ghashghaie
Samira.qashqaie.84@gmail.com
Saeed
Behzadi
behzadi.saeed@gmail.com
10.52547/jsri.16.1.121
Today, data is produced in large volumes, and from multiple sources, so this has caused problems in service. These problems can also affect the speed and accuracy of emergency services. Therefore, access to various resources and databases, information extraction to evaluate and analyze data and provide appropriate solutions for citizens is inevitable. In this paper evaluation of clusters is used for Getis-ord Gi* statistics and Anselin Local Moranchr('39')s I statistics to identify the behavioral pattern of data. The data used in this article is a large free dataset of Spatio-temporal emergency call events from the United States. Accidental call events in five years are evaluated from this dataset. Moran statistics are used to identify and detect the events which have the pattern of spatial distribution. A high/low distribution pattern of accidental events was obtained through Hotspot maps, an annual comparison and evaluation are made by survey the distribution map of events. Clustering Hotspots Map with Gi* statistics represents the spatial correlation between positive and negative events. In these distribution patterns, clusters with high value are called Hot-spots, and low-value clusters are called Cold-spots. Similarly, clustering maps of accidental events get evaluated every five years; then the Gi indicator evaluates each cluster for every two years. A positive z-score and G-index indicate that the data have a positive spatial correlation; its results show that the distribution pattern is similar in each year with an average of 93 percent. Then, hot/cold spot clustering maps of 5-year accidental events are also created with the general Moran indicator. Moreover, a confidence level is created after calculating the p-value and z-score. In all 5-year data calculations, the Moran coefficient of accidental events is greater than the expected coefficient. Evaluation of biennial clustering maps with Moran index showed that there is more than 96percent behavioral similarity of dispersion pattern in both years. Raster clustering maps are also created to evaluate the clustering of Moran and Gi indicates. The similarity of raster clusters is more than 95percent per year. The results show that the pattern of accident distribution is the same in 5 years. Although the number of accidents has decreased during this period, the hotspots of accidents have not changed significantly in the city. Furthermore, hotspots indicate a high density of accidental events with 95percent confidence in the study area, and most accidents occur on the South Claiborne and New Orleans highways and at intersections with major streets.
Clustering, spatial autocorrelation, accidental event, Getis-ord Gi* statistics, Anselin Morans I statistics.
http://jsri.srtc.ac.ir/article-1-353-en.html
http://jsri.srtc.ac.ir/article-1-353-en.pdf
Statistical Research and Training Center - Statistical Centre of Iran
Journal of Statistical Research of Iran JSRI
1735-1294
16
1
2019
9
1
Some New Results on the Preservation of Stochastic Orders and Aging Classes under Random Minima and Maxima
143
163
EN
Ebrahim
Salehi
salehi@birjandut.ac.ir
Ezzatollah
Gholami
ezzatgholami@birjandut.ac.ir
10.52547/jsri.16.1.143
In this paper, we obtain some results on preservation properties of the moment-generating-function and Laplace transform orders under the taking of random minima and maxima. Also, the reversed preservation of these stochastic orders is studied. In following, we investigate the closure of some new certain aging classes under the random minima and maxima.
Random minima (maxima), Life distribution class, Series (Parallel) system, Stochastic order, Reliability.
http://jsri.srtc.ac.ir/article-1-354-en.html
http://jsri.srtc.ac.ir/article-1-354-en.pdf
Statistical Research and Training Center - Statistical Centre of Iran
Journal of Statistical Research of Iran JSRI
1735-1294
16
1
2019
9
1
Estimation of Reliability of Stress-strength for a Kumaraswamy Distribution based on Progressively Censored Sample
165
209
EN
Akram
kohansal
kohansal@sci.ikiu.ac.ir
Ramin
Kazemi
r.kazemi@sci.ikiu.ac.ir
10.52547/jsri.16.1.165
The estimation of R=P(X<Y) in the case that X and Y are two independent Kumaraswamy distributed random variables with different parameters for progressively Type-II censored samples is studied. First assuming the same second shape parameters of two distributions, the maximum likelihood estimation and different confidence intervals are considered. Moreover, in case the second shape parameters of two distributions are known, MLE, UMVUE, Bayes estimation of R and confidence intervals are derived. Finally, the Maximum Likelihood and Bayes estimations of R in general case are obtained. Performance comparisons of different methods are carried out utilizing Monte Carlo simulations. Besides, the proposed approach is employed for reliability analysis on a real strength-stress dataset to demonstrate its application.
Kumaraswamy distribution, Progressive Type-II censoring, Bayesian estimator, Confidence interval, Monte Carlo simulation, Maximum likelihood estimator.
http://jsri.srtc.ac.ir/article-1-355-en.html
http://jsri.srtc.ac.ir/article-1-355-en.pdf
Statistical Research and Training Center - Statistical Centre of Iran
Journal of Statistical Research of Iran JSRI
1735-1294
16
1
2019
9
1
The Ability of Artificial Neural Networks in Learning Dependency of Spatial Data
211
228
EN
Abbas
Tavasoli
Tavassoli.a@birjand.ac.ir
Yadollah
Waghei
ywaghei@birjand.ac.ir
Alireza
Nazemi
nazemi20042003@gmail.com
10.52547/jsri.16.1.211
In conventional methods of spatial data analysis, such as Kriging, the dependency structure of data is estimated, modeled, and then used for data prediction. In contrast, the Artificial Neural Network (ANN) approach, which is a data-driven approach, does not model the data dependency structure. Therefore, an important question may arise here: Does ANN use, indirectly, spatial dependency structure in data prediction? In this paper, we want to answer this question through a simulation study. Different dependent and independent spatial data sets are simulated under two spatial structures, and the prediction accuracy of ANNs is compared for simulated data. It is shown that neural network error for predicting dependent spatial data is much less than that of independent spatial data. We conclude that the network can indirectly learn spatial dependence between the observations. We also applied the ANN method to an experimentally obtained data set and compared its prediction accuracy with Kriging as a common geostatistical method. The results showed that the neural network can be used as an alternative method for spatial data prediction.
Artificial Neural Networks, Spatial dependency, Spatial prediction.
http://jsri.srtc.ac.ir/article-1-356-en.html
http://jsri.srtc.ac.ir/article-1-356-en.pdf
Statistical Research and Training Center - Statistical Centre of Iran
Journal of Statistical Research of Iran JSRI
1735-1294
16
1
2019
9
1
On Dynamic Survival Past Extropy Properties
229
244
EN
Zohreh
Pakdaman
zpakdaman@hormozgan.ac.ir
Majid
Hashempour
ma.hashempour@hormozgan.ac.ir
10.52547/jsri.16.1.229
This paper deals with the dynamic survival past extropy as a measure of uncertainty in the past lifetime distributions. We introduce a quantile version of the extropy function in past lifetime. Various properties of the proposed measure are obtained. Additionally, some stochastic comparisons and bounds are derived and the performance of the dynamic survival past extropy of parallel and series system is studied as well.
Cumulative extropy, order statistics, past lifetime, quantile function, stochastic orders.
http://jsri.srtc.ac.ir/article-1-357-en.html
http://jsri.srtc.ac.ir/article-1-357-en.pdf
Statistical Research and Training Center - Statistical Centre of Iran
Journal of Statistical Research of Iran JSRI
1735-1294
16
1
2019
9
1
A Repetitive Sampling-based Control Chart for Multivariate Weighted Poisson Distribution with Two Different Indices
245
254
EN
Shohreh
Enami
enami1387@yahoo.com
Hamzeh
Torabi
hamzeh.torabi@gmail.com ©
10.52547/jsri.16.1.245
Control charts using repetitive group sampling have been an attractive topic in the last few years. This paper presents a control chart for multivariate weighed Poisson distribution by repetitive sampling with two different indexes. The effect of these two indexes on the performance of the control chart will be investigated based on the average sequence length criterion. Unlike almost all the research studies on this topic, this paper considers those cases in which the process parameters in the out-of-control situation are not necessarily a constant proportion of the process parameters in the control situation. In this paper, we will show that choosing appropriate statistics can be useful in the performance of the control chart and increasing its efficiency.
Multi-attribute process control, average run length, multivariate Poisson distribution, repetitive sampling.
http://jsri.srtc.ac.ir/article-1-358-en.html
http://jsri.srtc.ac.ir/article-1-358-en.pdf
Statistical Research and Training Center - Statistical Centre of Iran
Journal of Statistical Research of Iran JSRI
1735-1294
16
1
2019
9
1
Likelihood Inference in the Random Effects Logistic Regression Model with Response Misclassification and Covariate Subject to Measurement Error
255
286
EN
Maryam
Ahangari
m.ahangari@modares.ac.ir
Mousa
golalizadeh
golalizadeh@modares.ac.ir
Zahra
Rezaei Ghahroodi
z.rezaeigh@ut.ac.ir
10.52547/jsri.16.1.255
Generalized linear mixed models (GLMMs) are common methods for the analysis of clustered data. In many longitudinal and hierarchical epidemiological frameworks, accurate measurements of variables are invalid or expensive to be obtained and there might be situations that both the response and covariate variables are likely to be mismeasured. Insensitivity of errors in either covariate or response variable is, not always plausible. With nonlinear regression models for the outcome process, classification errors for binary responses and measurement error in covariates basically needs to be accounted for in order to make conclusive inferences. In this article, we provide an approach to simultaneously adjust for non-differential misclassification in the correlated binary response and classical measurement error in the covariates, using the multivariate Gauss-Hermite quadrature technique for the approximation of the likelihood function. Simulation studies are then conducted to inform the effects of correcting for measurement error and misclassification on the estimation of regression parameters. The application of the multivariate Gauss-Hermite quadrature method in the conjunction of measurement error and misclassification problems is further highlighted with real-world data based on a multilevel study of contraceptive methods used by women in Bangladesh.
Measurement Error, Binary Response, Multivariate Gauss-Hermite Quadrature, Random Effects Logistic Regression Model, Misclassification.
http://jsri.srtc.ac.ir/article-1-359-en.html
http://jsri.srtc.ac.ir/article-1-359-en.pdf