1
1726-4057
Iranian Statistical Society
279
The Beta Exponentiated Gumbel Distribution
Ownuk
J.
^{
b
}
^{
b
}Department of Statistics, Isfahan University, Isfahan, Iran.
1
12
2015
14
2
1
14
16
10
2014
18
01
2016
We introduce a new five-parameter distribution called the beta exponentiated Gumbel (BEG) distribution that includes the beta Gumbel, exponentiated Gumbel and Gumbel distribution. Expressions for the distribution function, density function and rth moment of the new distribution and order statistics are obtained. We discuss estimation of the parameters by maximum liklelihood and provide the information matrix. Using a real data set, we observe that the BEG distribution is flexible and can be used quite effectively in analysing positive data in place of the special cases.
276
Conditional Maximum Likelihood Estimation of the First-Order Spatial Integer-Valued Autoregressive (SINAR(1,1)) Model
Ghodsi
A.
^{
c
}
^{
c
}Department of Statistics, Faculty of Mathematics and Computer Sciences, Hakim Sabzevari University, Sabzevar, Iran.
1
12
2015
14
2
15
36
03
10
2014
30
01
2016
‎Recently a first-order Spatial Integer-valued Autoregressive‎ ‎SINAR(1,1) model was introduced to model spatial data that comes‎ ‎in counts citep{ghodsi2012}‎. ‎Some properties of this model‎ ‎have been established and the Yule-Walker estimator has been‎ ‎proposed for this model‎. ‎In this paper‎, ‎we introduce the‎ ‎conditional maximum likelihood method for estimating the‎ ‎parameters of the Poisson SINAR(1,1) model‎. ‎The asymptotic‎ ‎distribution of the estimators are also derived‎. ‎The properties of‎ ‎the Yule-Walker and conditional maximum likelihood estimators are‎ ‎compared by simulation study‎. ‎Finally‎, ‎the Student data citep{student1906} on‎ ‎the yeast cells count are used to illustrate the fitting of the‎ ‎SINAR(1,1) model‎.
307
Characterizations of Multivariate Normal-Poisson Model
Nisa
K.
^{
d
}
Kokonendji
C. C.
^{
e
}
Saefuddin
A.
^{
f
}
^{
d
} Lampung University, Bandar Lampung, Indonesia.
^{
e
}University of Franche-Comté, Besancon, France.
^{
f
} Bogor Agricultural University, Bogor, Indonesia.
1
12
2015
14
2
37
52
18
05
2015
02
04
2016
‎Multivariate normal-Poisson model has been recently introduced as a special case of normal stable Tweedie models‎. ‎The model is composed of a univariate Poisson variable‎, ‎and the remaining variables given the Poisson one are independent Gaussian variables with variance the value of the Poisson component‎. ‎Two characterizations of this model are shown‎, ‎first by variance function and then by generalized variance function which is the determinant of the variance function‎. ‎The latter provides an explicit solution of a particular Monge-Ampère equation.
312
Estimation of E(Y) from a Population with Known Quantiles
Zamanzade
E.
^{
g
}
Mohammad Ghasemi
H.
^{
h
}
^{
g
}Department of Statistics, University of Isfahan, Isfahan 81746-73441, Iran.
^{
h
}Department of Statistics, University of Isfahan, Isfahan 81746-73441, Iran.
1
12
2015
14
2
53
70
08
07
2015
05
05
2016
‎In this paper‎, ‎we consider the problem of estimating E(Y) based on a simple random sample when at least one of the population quantiles is known‎. ‎We propose a stratified estimator of E(Y)‎, ‎and show that it is strongly consistent‎. ‎We then establish the asymptotic normality of the suggested estimator‎, ‎and prove that it is asymptotically more efficient than the standard mean estimator in simple random sampling‎. ‎For finite sample sizes‎, ‎Monte Carlo simulation is used to show that the proposed method considerably improves the standard procedure‎. ‎Finally‎, ‎a real data example is used to illustrate the application of the proposed method‎.
325
60Exx: Distribution theory
A Flexible Class of Skew Logistic Distribution
Kumar
C. Satheesh
^{
i
}
Manju
L.
^{
j
}
^{
i
}Department of Statistics, University of Kerala, Trivandrum, Kerala, India.
^{
j
}Department of Community Medicine, Sree Gokulam Medical College, Trivandrum, Kerala, India.
1
12
2015
14
2
71
92
11
11
2015
05
05
2016
‎Here we consider a new class of skew logistic distribution as a generalized mixture of the standard logistic and skew logistic distributions‎, ‎and study some of its important aspects‎. ‎The tail behaviour of the distribution is compared with that of the skew logistic distribution and a location-scale extension of the distribution is proposed‎. ‎Further the maximum likelihood estimation of the parameters of the extended class of distribution is attempted. The usefulness of the proposed class of distribution is illustrated with the help of a data set‎.
338
60Exx: Distribution theory
A New Modification in the Classical Laplace Distribution
Mahmoudvand
R
^{
k
}
Faradmal
J
^{
l
}
Abbasi
N
^{
m
}
Lurz
K
^{
n
}
^{
k
}Department of Statistics, Bu-Ali Sina University, Hamedan, Iran.
^{
l
}Modelling of Noncommunicable Diseases Research Center and Department of Biostatistics, School of Public Health, Hamadan University of Medical Sciences, Hamedan, Iran.
^{
m
}Department of Statistics, Payame Noor University, I. R., Iran.
^{
n
}prognostica GmbH, Wurzburg, Germany
1
12
2015
14
2
93
118
02
01
2016
25
05
2016
‎Several modifications of the Laplace distribution have been introduced and applied in various fields up to this day‎. ‎In this paper‎, ‎we introduce a modified symmetric version of the classical Laplace distribution‎. ‎We provide a comprehensive theoretical description of this distribution‎. ‎In particular‎, ‎we derive the formulas for the $k$th moment‎, ‎quantiles and several useful alternative representations of the distribution‎. ‎We derive the maximum likelihood estimators of the parameters and investigate their properties via simulation‎. ‎Finally‎, ‎we analyse three real-world datasets to illustrate the usefulness of the modified classical Laplace distribution‎. ‎The results suggest that further improvement to classical Laplace distribution fitting is possible and the new model provides an attractive alternative to the classical Laplace distribution.