scholarly journals Estimation of parameters of Nadarajah-Haghighi extension of the exponential distribution using perfect and imperfect ranked set sample

2020 ◽  
Vol 30 (2) ◽  
pp. 177-198
Author(s):  
Marija Minic
Keyword(s):  
Maximum Likelihood ◽  
Exponential Distribution ◽  
Maximum Likelihood Method ◽  
Likelihood Method ◽  
Simple Random Sample ◽  
Estimation Of Parameters ◽  
Ranked Set Sample ◽  
Scale Parameters ◽  
Wide Range ◽  
Mean Square Errors

The ranked set sampling (RSS) is a cost-effective method of sampling that can be used in a wide range of statistical problems. In this paper, the shape and the scale parameters of Nadarajah-Haghighi extension of the exponential distribution are estimated based on a simple random sample (SRS) and RSS. Three cases are considered: 1) the scale parameter is known; 2) the shape parameter is known; 3) both shape and scale parameters are unknown. Observations are done when the ranking mechanism in the ranked set sample is perfect and when it is not. Method of moments, the maximum likelihood method, and a modification of the maximum likelihood method are used. The obtained estimators are compared in terms of their biases and mean square errors (MSE). The results revealed that estimators based on RSS tend to show better properties (smaller bias and MSE) relative to their SRS counterparts, regardless of the quality of the ranking.

scholarly journals Estimation of P(Y < X) in a Four-Parameter Generalized Gamma Distribution

2016 ◽  
Vol 41 (3) ◽  
Author(s):  
M. Masoom Ali ◽  
Manisha Pal ◽  
Jungsoo Woo
Keyword(s):  
Maximum Likelihood ◽  
Closed Form ◽  
Importance Sampling ◽  
Simulation Study ◽  
Maximum Likelihood Method ◽  
Sampling Procedure ◽  
Likelihood Method ◽  
Scale Parameters ◽  
Generalized Gamma ◽  
Modified Maximum Likelihood

In this paper we consider estimation of R = P(Y < X), when X and Y are distributed as two independent four-parameter generalized gamma random variables with same location and scale parameters. A modified maximum likelihood method and a Bayesian technique have been used to estimate R on the basis of independent samples. As the Bayes estimator cannot be obtained in a closed form, it has been implemented using importance sampling procedure. A simulation study has also been carried out to compare the two methods.

scholarly journals On the Estimation of Parameter of Weighted Sums of Exponential Distribution

2014 ◽  
Vol 2014 ◽  
pp. 1-3
Author(s):  
N. Abbasi ◽  
A. Namju ◽  
N. Safari
Keyword(s):  
Maximum Likelihood ◽  
Exponential Distribution ◽  
Mean Square Error ◽  
Moment Method ◽  
Maximum Likelihood Method ◽  
Random Variable ◽  
Likelihood Method ◽  
Weighted Sums ◽  
Mean Square ◽  
The Mean

The random variable Zn,α=Y1+2αY2+⋯+nαYn, with α∈ℝ and Y1,Y2,…  being independent exponentially distributed random variables with mean one, is considered. Van Leeuwaarden and Temme (2011) attempted to determine good approximation of the distribution of Zn,α. The main problem is estimating the parameter α that has the main state in applicable research. In this paper we show that estimating the parameter α by using the relation between α and mode is available. The mean square error values are obtained for estimating α by mode, moment method, and maximum likelihood method.

Fracture spacing and its relation to bed thickness

1989 ◽  
Vol 126 (4) ◽  
pp. 355-362 ◽  
Author(s):  
Qin Huang ◽  
J. Angelier
Keyword(s):  
Maximum Likelihood ◽  
Exponential Distribution ◽  
Maximum Likelihood Method ◽  
Likelihood Method ◽  
Gulf Of Suez ◽  
Joint Spacing ◽  
Fracture Spacing ◽  
Negative Exponential Distribution ◽  
Bed Thickness ◽  
Negative Exponential

AbstractUsing examples from the Gulf of Suez and southeastern France, the distribution of tension tectonic joints as well as shear tectonic joints in continuous profiles is shown to fit a Gamma distribution. The parameters of this distribution are determined using the maximum likelihood method. Apparent fit with negative exponential distribution in photointerpretation analysis results from lack of resolution. The average joint spacing is directly proportional to bed thickness; it decreases when the degree of rock consolidation increases.

scholarly journals Quartile Method Estimation of Two-Parameter Exponential Distribution Data with Outliers

2016 ◽  
Vol 5 (5) ◽  
pp. 12
Author(s):  
Entisar A. Elgmati ◽  
Nadia B. Gregni
Keyword(s):  
Maximum Likelihood ◽  
Exponential Distribution ◽  
Simulation Study ◽  
Maximum Likelihood Method ◽  
Likelihood Method ◽  
Distribution Data ◽  
Unknown Parameters ◽  
First Order ◽  
Minimum Statistics ◽  
Two Parameter

Several methods have been used to estimate the unknown parameters in the two-parameter exponential distribution. Here we have considered two of these methods, maximum likelihood method and median-first order statistics method. However, in the presence of outliers these methods are not valid. In this paper we propose two approaches that deal with this situation. The idea is based on using first and third quartile instead of the minimum statistics. We investigated the parameters estimate using these methods through simulation study. The new method gives similar results under the normal situation and much better results when the data has outliers.

scholarly journals Some Properties and Estimation of Parameters for the Five Parameter Type I Generalized Half Logistic Distribution under Complete Observation

2020 ◽  
pp. 39-46
Author(s):  
O. A. Bello ◽  
P. O. Awodutire ◽  
I. Sule ◽  
H. O. Lawal
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Likelihood Method ◽  
Logistic Distribution ◽  
Type I ◽  
Lifetime Data ◽  
Estimation Of Parameters ◽  
Distribution Estimation ◽  
Complete Observation

This paper is a further study of the five parameter type I generalized half logistic distribution. We derived some properties of the distribution. Estimation of the parameters of the distribution under complete observation was studied using the maximum likelihood method. To assess the flexibility of the distribution, it was applied to a real lifetime data and the results when compared to the sub-models showed that the five parameter type I generalized half logistic distribution performed best.

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