scholarly journals T-Inverse Exponential Family Of Distributions

2021 ◽  
Vol 23 (09) ◽  
pp. 556-572
Author(s):  
Mahmoud Riad Mahmoud ◽  
◽  
Moshera A.M. Ahmad ◽  
AzzaE. Ismail ◽  
◽  
...  
Keyword(s):  
Exponential Family ◽  
Quantile Function ◽  
Mean Deviation ◽  
Alpha Power ◽  
Special Model ◽  
Quantile Functions ◽  
Distribution Family ◽  
Exponential Family Of Distributions ◽  
Y Family ◽  
Family Of Distributions

Recently, several methods have been introduced to generate neoteric distributions with more exibility, like T-X, T-R [Y] and alpha power. The T-Inverse exponential [Y] neoteric family of distributons is proposed in this paper utilising the T-R [Y] method. A generalised inverse exponential (IE) distribution family has been established. The distribution family is generated using quantile functions of some dierent distributions. A number of general features in the T-IE [Y] family are examined, like mean deviation, mode, moments, quantile function, and entropies. A special model of the T-IE [Y] distribution family was one of those old distributions. Certain distribution examples are produced by the T-IE [Y] family. An applied case was presented which showed the importance of the neoteric family.

scholarly journals Asymptotic approximations to the Bayes posterior risk

1990 ◽  
Vol 3 (2) ◽  
pp. 99-116
Author(s):  
Toufik Zoubeidi
Keyword(s):  
Parameter Space ◽  
Exponential Family ◽  
Distribution Functions ◽  
Independent Random Variables ◽  
Asymptotic Approximations ◽  
Prior Density ◽  
Posterior Probabilities ◽  
Exponential Family Of Distributions ◽  
Family Of Distributions ◽  
Convex Subsets

Suppose that, given ω=(ω1,ω2)∈ℜ2, X1,X2,… and Y1,Y2,… are independent random variables and their respective distribution functions Gω1 and Gω2 belong to a one parameter exponential family of distributions. We derive approximations to the posterior probabilities of ω lying in closed convex subsets of the parameter space under a general prior density. Using this, we then approximate the Bayes posterior risk for testing the hypotheses H0:ω∈Ω1 versus H1:ω∈Ω2 using a zero-one loss function, where Ω1 and Ω2 are disjoint closed convex subsets of the parameter space.

9. Models for Generalized Location Systems

2007 ◽  
Vol 37 (1) ◽  
pp. 283-348 ◽  
Author(s):  
Carter T. Butts
Keyword(s):  
Exponential Family ◽  
Social Systems ◽  
System Model ◽  
Social Phenomena ◽  
Location System ◽  
Formal Framework ◽  
Model Complex ◽  
Exponential Family Of Distributions ◽  
Residential Settlement ◽  
Family Of Distributions

A formal framework is introduced for a general class of assignment systems that can be used to characterize a range of social phenomena. An exponential family of distributions is developed for modeling such systems, allowing for the incorporation of both attributional and relational covariates. Methods are shown for simulation and inference using the location system model. Two illustrative applications (occupational stratification and residential settlement patterns) are presented, and simulation is employed to show the behavior of the location system model in each case; a third application, involving occupancy of positions within an organization, is used to demonstrate inference for the location system. By leveraging established results in the fields of social network analysis, spatial statistics, and statistical mechanics, it is argued that sociologists can model complex social systems without sacrificing inferential tractability.

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