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Distributed Generators
Exponential Distribution
Gamma Distribution
Maximum Entropy
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On families of beta and generalized gammagenerated distributions and associated inference
On families of beta and generalized gammagenerated distributions and associated inference,10.1016/j.stamet.2008.12.003,Statistical Methodology,K. Zo
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On families of beta and generalized gammagenerated distributions and associated inference
(
Citations: 7
)
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K. Zografos
,
N. Balakrishnan
A general family of univariate distributions generated by beta random variables, proposed by Jones, has been discussed recently in the literature. This family of distributions possesses great flexibility while fitting symmetric as well as skewed models with varying tail weights. In a similar vein, we define here a family of univariate distributions generated by Stacy’s generalized gamma variables. For these two families of univariate distributions, we discuss
maximum entropy
characterizations under suitable constraints. Based on these characterizations, an expected ratio of quantile densities is proposed for the discrimination of members of these two broad families of distributions. Several special cases of these results are then highlighted. An alternative to the usual method of moments is also proposed for the estimation of the parameters, and the form of these estimators is particularly amenable to these two families of distributions.
Journal:
Statistical Methodology
, vol. 6, no. 4, pp. 344362, 2009
DOI:
10.1016/j.stamet.2008.12.003
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Citation Context
(5)
...One may ask: when we choose one over the other? We will answer this question for arbitrary parent distribution by following a method proposed by Zografos and Balakrishnan
18
...
Saralees Nadarajah
,
et al.
A new family of lifetime models
...Recently, Zografos and Balakrishnan
1
have introduced a new family of distributions generated by gamma random variables...
Miroslav M. Ristić
,
et al.
The gammaexponentiated exponential distribution
...Recently, Zografos and Balakrishnan
1
have introduced a new family of distributions generated by gamma random variables...
Miroslav M. Ristić
,
et al.
The gammaexponentiated exponential distribution
...New, broad families of probability distributions have been proposed and studied in the recent literature (see, for example, [1], [2], [
3
] and references therein)...
K. Zografos
,
et al.
Generalized families of univariate distributions
...This representation of X helps to generate random numbers from (1) while the case α = β = 1 corresponds to the wellknown quantile function representation X = F −1 (U ), where U ∼ U (0, 1), which is used in order to generate data from a distribution F . The family (1) has been recently studied by Zografos and Balakrishnan [
24
]...
...Name of the distribution Authors / Year BetaNormal Eugene et al. [6] BetaLogistic Brown et al. [5] and Olapade [20] BetaFrechet Nadarajah and Gupta [17] BetaGumbel Nadarajah and Kotz [18] BetaExponential Nadarajah and Kotz [19] BetaGamma Kong et al. [12] BetaWeibull Lee et al. [13] and Zografos [23] BetaPareto Akinsete et al. [3] BetaPower Zografos and Balakrishnan [
24
] BetaGeneralized Half Normal Pescim et al. [22] ...
...kα x kα−1 � 1 − (θx) k � β−1 ,0
24])...
...This permits the development of an alternative to the method of moments estimation procedure, as it is described in Zografos and Balakrishnan [
24
]...
...bution F and the parent density f . This term plays a key role to introduce a test for discriminating between the members of the GBGII distribution, in a manner similar to that which is developed in Zografos and Balakrishnan [
24
]...
Kostas Zografos
.
Generalized Beta GeneratedII Distributions
References
(21)
Families of distributions arising from distributions of order statistics
(
Citations: 52
)
M. C. Jones
Journal:
Test
, vol. 13, no. 1, pp. 143, 2004
On a Class of Distributions Defined by the Relationship Between Their Density and Distribution Functions
(
Citations: 4
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M. C. Jones
Journal:
Communications in Statisticstheory and Methods  COMMUN STATISTTHEOR METHOD
, vol. 36, no. 10, pp. 18351843, 2007
BETANORMAL DISTRIBUTION AND ITS APPLICATIONS
(
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Nicholas Eugene
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Journal:
Communications in Statisticstheory and Methods  COMMUN STATISTTHEOR METHOD
, vol. 31, no. 4, pp. 497512, 2002
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(
Citations: 5
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M. C. Jones
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Journal:
Biometrika
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The beta exponential distribution
(
Citations: 34
)
Saralees Nadarajah
,
Samuel Kotz
Journal:
Reliability Engineering & System Safety  RELIAB ENG SYST SAFETY
, vol. 91, no. 6, pp. 689697, 2006
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Citations
(7)
A new family of lifetime models
Saralees Nadarajah
,
K. Jayakumar
,
Miroslav M. Ristić
Journal:
Journal of Statistical Computation and Simulation  J STAT COMPUT SIM
, vol. aheadofp, no. aheadofp, pp. 116, 2012
The gammaexponentiated exponential distribution
Miroslav M. Ristić
,
Narayanaswamy Balakrishnan
Journal:
Journal of Statistical Computation and Simulation  J STAT COMPUT SIM
, vol. 82, no. 8, pp. 11911206, 2012
A compound class of Weibull and power series distributions
(
Citations: 1
)
Alice Lemos Morais
,
Wagner BarretoSouza
Journal:
Computational Statistics & Data Analysis  CS&DA
, vol. 55, no. 3, pp. 14101425, 2011
The gammaexponentiated exponential distribution
(
Citations: 1
)
Miroslav M. Ristić
,
Narayanaswamy Balakrishnan
Journal:
Journal of Statistical Computation and Simulation  J STAT COMPUT SIM
, vol. aheadofp, no. aheadofp, pp. 116, 2011
A new skew generalization of the normal distribution: Properties and applications
(
Citations: 2
)
V. J. García
,
E. GómezDéniz
,
F. J. VázquezPolo
Journal:
Computational Statistics & Data Analysis  CS&DA
, vol. 54, no. 8, pp. 20212034, 2010