Strong consistency of the MLE under two-parameter Gamma mixture models with a structural scale parameter

2021 ◽  
Author(s):  
Mingxing He ◽  
Jiahua Chen
Keyword(s):  
Mixture Models ◽  
Strong Consistency ◽  
Scale Parameter ◽  
Structural Scale ◽  
Two Parameter

Estimation of a scale parameter in mixture models with unknown location

2005 ◽  
Vol 128 (1) ◽  
pp. 191-218 ◽  
Author(s):  
Constantinos Petropoulos ◽  
Stavros Kourouklis
Keyword(s):  
Mixture Models ◽  
Scale Parameter

Lifetime Estimation for Web Game Based on Weibull Distribution

2014 ◽  
Vol 539 ◽  
pp. 456-459
Author(s):  
Hai Shu Yu ◽  
Yan Hua Yuan
Keyword(s):  
Weibull Distribution ◽  
Shape Parameter ◽  
Scale Parameter ◽  
Likelihood Estimation ◽  
Statistic Analysis ◽  
Lifetime Data ◽  
Lifetime Estimation ◽  
Proposed Model ◽  
Two Parameter ◽  
The Web

In order to make statistic analysis on lifetime data for web game, the two-parameter Weibull distribution was applied to describe its distribution. The shape parameter and the scale parameter were given by maximum likelihood estimation. When a web game followed Weibull distribution, the lifetime parameters are calculated via Matlab. The results show that the proposed model is appropriate to estimate the web game lifetime.

scholarly journals Estimation of the scale parameter of gamma model in presence of outlier observations

1990 ◽  
Vol 13 (1) ◽  
pp. 121-127 ◽  
Author(s):  
M. E. Ghitany
Keyword(s):  
Shape Parameter ◽  
Scale Parameter ◽  
Point Estimation ◽  
Random Shape ◽  
Gamma Model ◽  
Squared Error Loss Function ◽  
Squared Error Loss ◽  
Testing Model ◽  
Squared Error ◽  
Two Parameter

This paper considers the Bayesian point estimation of the scale parameter for a two-parameter gamma life-testing model in presence of several outlier observations in the data. The Bayesian analysis is carried out under the assumption of squared error loss function and fixed or random shape parameter.

scholarly journals Interval Estimations of the Two-Parameter Exponential Distribution

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Lai Jiang ◽  
Augustine C. M. Wong
Keyword(s):  
Exponential Distribution ◽  
Scale Parameter ◽  
Real Life ◽  
Simulation Studies ◽  
Threshold Parameter ◽  
Predictive Density ◽  
Data Set ◽  
Interval Estimates ◽  
Real Life Data ◽  
Two Parameter

In applied work, the two-parameter exponential distribution gives useful representations of many physical situations. Confidence interval for the scale parameter and predictive interval for a future independent observation have been studied by many, including Petropoulos (2011) and Lawless (1977), respectively. However, interval estimates for the threshold parameter have not been widely examined in statistical literature. The aim of this paper is to, first, obtain the exact significance function of the scale parameter by renormalizing thep∗-formula. Then the approximate Studentization method is applied to obtain the significance function of the threshold parameter. Finally, a predictive density function of the two-parameter exponential distribution is derived. A real-life data set is used to show the implementation of the method. Simulation studies are then carried out to illustrate the accuracy of the proposed methods.

Consistency of the penalized MLE for two-parameter gamma mixture models

2016 ◽  
Vol 59 (12) ◽  
pp. 2301-2318 ◽  
Author(s):  
JiaHua Chen ◽  
ShaoTing Li ◽  
XianMing Tan
Keyword(s):  
Mixture Models ◽  
Two Parameter

scholarly journals On extreme daily precipitation totals at Athens, Greece

2007 ◽  
Vol 10 ◽  
pp. 59-66 ◽  
Author(s):  
P. T. Nastos ◽  
C. S. Zerefos
Keyword(s):  
Daily Precipitation ◽  
Scale Parameter ◽  
Positive Trend ◽  
Loss Of Life ◽  
Environmental Consequences ◽  
Extreme Precipitation Events ◽  
Significant Difference ◽  
Precipitation Records ◽  
Two Parameter ◽  
Precipitation Events

Abstract. The paper studies changes in daily precipitation records at the National Observatory, Athens, during the period 1891–2004. This is the longest available time series of precipitation for Greece. The results show that both the shape and scale parameter of a fitted two parameter gamma distribution for the last two decades do show a significant difference of these parameters, when compared to any previous period from the 1890s through the 1970s. Also important changes are observed in daily precipitation totals exceeding various thresholds such as 10, 20, 30 and 50 mm. More specifically, a negative trend in the number of wet days (remarkable after 1968) and a positive trend in extreme daily precipitation are evident. The changes of heavy and extreme precipitation events in this part of SE Europe have significant environmental consequences which cause considerable damage and loss of life.

scholarly journals A two-parameter extension of Urbanik’s product convolution semigroup

2019 ◽  
Vol 39 (2) ◽  
pp. 441-458
Author(s):  
Christian Berg
Keyword(s):  
Scale Parameter ◽  
Gumbel Distribution ◽  
Convolution Semigroup ◽  
Probability Measures ◽  
Moment Sequence ◽  
Infinitely Divisible ◽  
Probability Densities ◽  
Special Case ◽  
Two Parameter ◽  
Positive Half

We prove that sna, b = Γan + b/Γb, n = 0, 1, . . ., is an infinitely divisible Stieltjes moment sequence for arbitrary a, b > 0. Its powers sna, bc, c > 0, are Stieltjes determinate if and only if ac ≤ 2. The latter was conjectured in a paper by Lin 2019 in the case b = 1. We describe a product convolution semigroup τca, b, c > 0, of probability measures on the positive half-line with densities eca, b and having the moments sna, bc. We determine the asymptotic behavior of eca, bt for t → 0 and for t → ∞, and the latter implies the Stieltjes indeterminacy when ac > 2. The results extend the previous work of the author and Lopez 2015 and lead to a convolution semigroup of probability densities gca, bxc>0 on the real line. The special case gca, 1xc>0 are the convolution roots of the Gumbel distribution with scale parameter a > 0. All the densities gca, bx lead to determinate Hamburger moment problems.

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