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## An Extended Exponentiated Exponential Distribution and its Properties

### Citations

4015 |
Non-parametric estimation from incomplete observation.
- EL, Meier
- 1958
(Show Context)
Citation Context ...ess of carbon fibers whose survival times, uncensored data, are available. Retable the n survival times in order of increasing magnitude such that t1 ≤ t2 ≤ ... ≤ tn. The Kaplan-Meier estimator (KME) =-=[9]-=-, also known as the product limit estimator, of a sf is defined as: Ḡn(t) = ∏ t:ti≤t 1− δ(i) n− i+ 1 , t > 0. Figure 3 show the p−p plot of the EE versus the fittedMOEEE sf for the given data. Visual... |

262 |
Fitting Autoregressive Models for Prediction.”
- Akaike
- 1969
(Show Context)
Citation Context ...(BIC) defined as: AIC = loglikelihood− 2k BIC = loglikelihood− k 2 log(n) where k is the number of parameters in the model and n is the sample size. For more details about the AIC and BIC, see Akiake =-=[3]-=- and Schwarz et al [17], respectively. The model with higher AIC (BIC) is the one that better fits the data. 7. APPLICATION In this section, we fit theMOEEE distribution to a real data set. This data ... |

32 |
A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families.
- Marshall, Olkin
- 1997
(Show Context)
Citation Context ...,9 Abdel-Hamid and Al-Hussaini [1], Kundu and Pradhan [10] and Aslam et al. [4]. Some generalizations of the EE distribution are discussed in Nadarajah and Kotz [13]. On the other hand, MarshallOlkin =-=[12]-=- defined a technique of generalization for a given probability distribution increasing the number of parameters by one. The new parameter results a flexibility in the distribution and known as the Mar... |

25 |
Inferences for generalized exponential distribution based on record statistics,
- Raqab
- 2002
(Show Context)
Citation Context ...hree families, Gamma, Weibull and the EE are generalization of the exponential family but in different ways. Many authors derived other properties of the (EE) distribution, Gupta and Kundu [7], Raqab =-=[16]-=-, Zheng [22], Shirke et al. [18],9 Abdel-Hamid and Al-Hussaini [1], Kundu and Pradhan [10] and Aslam et al. [4]. Some generalizations of the EE distribution are discussed in Nadarajah and Kotz [13]. O... |

11 |
The generalized Gompertz verhulst family distriutions,
- Ahuja, Nash
- 1979
(Show Context)
Citation Context ...ution, Compound distribution, Geometric extreme stability, AIC, BIC, Likelihood ratio test, P-P plot, mean residual life 1. INTRODUCTION The two parameter EE distribution introduced by Ahuja and Nash =-=[2]-=- and further, studied by Gupta and Kundu[6]. This distribution has shape and scale parameters like Gamma and Weibull distributions. Moreover it has better fit than Weibull and Gamma in many cases, Raj... |

11 |
et al. “Estimating the dimension of a model”. In: The annals of statistics 6.2
- Schwarz
- 1978
(Show Context)
Citation Context ...= loglikelihood− 2k BIC = loglikelihood− k 2 log(n) where k is the number of parameters in the model and n is the sample size. For more details about the AIC and BIC, see Akiake [3] and Schwarz et al =-=[17]-=-, respectively. The model with higher AIC (BIC) is the one that better fits the data. 7. APPLICATION In this section, we fit theMOEEE distribution to a real data set. This data set is an uncensored da... |

10 |
A bootstrap control chart for Weibull Percentiles
- Nichols, Padgett
- 2006
(Show Context)
Citation Context ...igher AIC (BIC) is the one that better fits the data. 7. APPLICATION In this section, we fit theMOEEE distribution to a real data set. This data set is an uncensored data set from Nichols and Padgett =-=[14]-=-consisting of 100 observations on breaking stress of carbon fibers (in Gba) given in table 1. Table 1. : 100 observations on breaking stress of carbon fibers (in Gba) 3.7 2.74 2.73 2.5 3.6 3.11 3.27 2... |

10 |
On the Fisher information matrix in type-II censored data from the exponentiaed exponetial family.
- Zheng
- 2002
(Show Context)
Citation Context ...s, Gamma, Weibull and the EE are generalization of the exponential family but in different ways. Many authors derived other properties of the (EE) distribution, Gupta and Kundu [7], Raqab [16], Zheng =-=[22]-=-, Shirke et al. [18],9 Abdel-Hamid and Al-Hussaini [1], Kundu and Pradhan [10] and Aslam et al. [4]. Some generalizations of the EE distribution are discussed in Nadarajah and Kotz [13]. On the other ... |

8 |
The Exponentiated Type Distributions".
- Nadarajah, Kotz
- 2006
(Show Context)
Citation Context ...ab [16], Zheng [22], Shirke et al. [18],9 Abdel-Hamid and Al-Hussaini [1], Kundu and Pradhan [10] and Aslam et al. [4]. Some generalizations of the EE distribution are discussed in Nadarajah and Kotz =-=[13]-=-. On the other hand, MarshallOlkin [12] defined a technique of generalization for a given probability distribution increasing the number of parameters by one. The new parameter results a flexibility i... |

4 |
On the Possibility of Improving the Mean Useful Life of Items by Eliminating those with Short Lives
- WATSON, WELLS
- 1961
(Show Context)
Citation Context ... curves for the MOEEE distribution for selected values of the parameters α, β and λ. Another ageing property for MOEEE distribution is the mean residual life (mrl), was introduced by Watson and Wells =-=[20]-=- to analyse burn-in problems, has been studied by reliabilists, statisticians, survival analysts and others. Its defined simply as the expected value of the remaining lifetime beyond an age t. If X is... |

3 |
and Debasis Kundu. Generalized exponential distribution: Existing results and some recent developments
- Gupta
(Show Context)
Citation Context ...reme stability, AIC, BIC, Likelihood ratio test, P-P plot, mean residual life 1. INTRODUCTION The two parameter EE distribution introduced by Ahuja and Nash [2] and further, studied by Gupta and Kundu=-=[6]-=-. This distribution has shape and scale parameters like Gamma and Weibull distributions. Moreover it has better fit than Weibull and Gamma in many cases, Raja and Mir[15]. The applications of the EE d... |

3 | Bayesian inference and life testing plans for generalized exponential distribution”,
- Kundu, Pradhan
- 2009
(Show Context)
Citation Context ...in different ways. Many authors derived other properties of the (EE) distribution, Gupta and Kundu [7], Raqab [16], Zheng [22], Shirke et al. [18],9 Abdel-Hamid and Al-Hussaini [1], Kundu and Pradhan =-=[10]-=- and Aslam et al. [4]. Some generalizations of the EE distribution are discussed in Nadarajah and Kotz [13]. On the other hand, MarshallOlkin [12] defined a technique of generalization for a given pro... |

3 |
The use of mixed distribution models to determine bout criteria for the analysis of animal behaviour.
- Yeates, Tolkamp, et al.
- 2001
(Show Context)
Citation Context ...l and Gamma in many cases, Raja and Mir[15]. The applications of the EE distribution have been widespread, we mention: models to determine bout criteria for analysis of animal behavior, Yeates et al. =-=[21]-=-; software reliability growth models for vital quality metrics, Subburaj et al. [11]; models for episode peak and duration for eco-hydro-climatic applications, Biondi et al.[5]; and cure rate modeling... |

2 | Time truncated acceptance sampling plans for generalized exponential distribution
- Aslam, Kundub, et al.
- 2010
(Show Context)
Citation Context ...y authors derived other properties of the (EE) distribution, Gupta and Kundu [7], Raqab [16], Zheng [22], Shirke et al. [18],9 Abdel-Hamid and Al-Hussaini [1], Kundu and Pradhan [10] and Aslam et al. =-=[4]-=-. Some generalizations of the EE distribution are discussed in Nadarajah and Kotz [13]. On the other hand, MarshallOlkin [12] defined a technique of generalization for a given probability distribution... |

2 |
The generalized exponential cure rate model with covariates”,
- Kannan, Kundu, et al.
- 2010
(Show Context)
Citation Context ...bility growth models for vital quality metrics, Subburaj et al. [11]; models for episode peak and duration for eco-hydro-climatic applications, Biondi et al.[5]; and cure rate modeling, Kannan et al. =-=[8]-=-. An absolutely continuous random variable (rv) is said to have TheEE distribution if its survival function (sf) and its probability density function (pdf ) are given by, F̄ (x) = 1− (1− e−βx)α, (1) f... |

2 |
On extension of some exponentiated distributions with application
- Raja, Mir
(Show Context)
Citation Context ...her, studied by Gupta and Kundu[6]. This distribution has shape and scale parameters like Gamma and Weibull distributions. Moreover it has better fit than Weibull and Gamma in many cases, Raja and Mir=-=[15]-=-. The applications of the EE distribution have been widespread, we mention: models to determine bout criteria for analysis of animal behavior, Yeates et al. [21]; software reliability growth models fo... |

1 |
and Essam K AL-Hussaini. Estimation in step-stress accelerated life tests for the exponentiated exponential distribution with type-I censoring
- Abdel-Hamid
(Show Context)
Citation Context ...exponential family but in different ways. Many authors derived other properties of the (EE) distribution, Gupta and Kundu [7], Raqab [16], Zheng [22], Shirke et al. [18],9 Abdel-Hamid and Al-Hussaini =-=[1]-=-, Kundu and Pradhan [10] and Aslam et al. [4]. Some generalizations of the EE distribution are discussed in Nadarajah and Kotz [13]. On the other hand, MarshallOlkin [12] defined a technique of genera... |

1 |
A new stochastic model of episode peak and duration for eco-hydro-climatic applications. ecological modelling
- Biondi, Kozubowski, et al.
(Show Context)
Citation Context ...ehavior, Yeates et al. [21]; software reliability growth models for vital quality metrics, Subburaj et al. [11]; models for episode peak and duration for eco-hydro-climatic applications, Biondi et al.=-=[5]-=-; and cure rate modeling, Kannan et al. [8]. An absolutely continuous random variable (rv) is said to have TheEE distribution if its survival function (sf) and its probability density function (pdf ) ... |

1 |
and Mohammad Z Raqab. Bayesian prediction of rainfall records using the generalized exponential distribution
- Madi
(Show Context)
Citation Context ... have been widespread, we mention: models to determine bout criteria for analysis of animal behavior, Yeates et al. [21]; software reliability growth models for vital quality metrics, Subburaj et al. =-=[11]-=-; models for episode peak and duration for eco-hydro-climatic applications, Biondi et al.[5]; and cure rate modeling, Kannan et al. [8]. An absolutely continuous random variable (rv) is said to have T... |

1 | Tolerance intervals for exponentiated scale family of distributions
- Shirke, Kumbhar, et al.
- 2005
(Show Context)
Citation Context ...d the EE are generalization of the exponential family but in different ways. Many authors derived other properties of the (EE) distribution, Gupta and Kundu [7], Raqab [16], Zheng [22], Shirke et al. =-=[18]-=-,9 Abdel-Hamid and Al-Hussaini [1], Kundu and Pradhan [10] and Aslam et al. [4]. Some generalizations of the EE distribution are discussed in Nadarajah and Kotz [13]. On the other hand, MarshallOlkin ... |

1 |
Abhimanyu Singh Yadav. Parameter estimation in marshall-olkin exponential distribution under type-i hybrid censoring scheme
- Singh, Singh
(Show Context)
Citation Context ...x)α + λ)2 , x > 0. (5) TheMOEEE distribution having exponential, EE and MarshallOlkin extended exponential (MOEE) distributions as sub-models: (1) If α = 1, we have the MOEE distribution, Singh et al =-=[19]-=-. (2) If λ = 1 we get the EE distribution, Gupta and Kundu [6]. (3) If λ = 1, α = 1 we get the exponential distribution. The following theorem gives simple conditions under which the pdf(6) is decreas... |