Proper Bayes minimax estimation of parameters of Poisson distributions in the presence of unbalanced sample sizes

2020 ◽  
Vol 34 (4) ◽  
pp. 728-751
Author(s):  
Yasuyuki Hamura ◽  
Tatsuya Kubokawa
Keyword(s):  
Minimax Estimation ◽  
Sample Sizes ◽  
Estimation Of Parameters ◽  
Poisson Distributions

Determination of Optimal Sample Sizes in the Beta-Binomial Brand Choice Model

1980 ◽  
Vol 17 (1) ◽  
pp. 58-62 ◽  
Author(s):  
Moshe M. Givon
Keyword(s):  
Stochastic Models ◽  
Choice Behavior ◽  
Choice Model ◽  
Brand Choice ◽  
Binomial Model ◽  
Sample Sizes ◽  
Estimation Of Parameters ◽  
Optimal Sample

Estimation of parameters in stochastic models of brand choice behavior requires the determination of two sample sizes: the number of consumers and the number of purchase occasions observed for each consumer. A method for determination of optimal sample sizes is presented and illustrated by an application to the beta-binomial model.

scholarly journals Exact values and sharp estimates for the total variation distance between binomial and Poisson distributions

2008 ◽  
Vol 40 (4) ◽  
pp. 1033-1047 ◽  
Author(s):  
José A. Adell ◽  
José M. Anoz ◽  
Alberto Lekuona
Keyword(s):  
Total Variation ◽  
Efficient Algorithm ◽  
Total Variation Distance ◽  
Sample Sizes ◽  
Charlier Polynomials ◽  
Sharp Estimates ◽  
Poisson Distributions ◽  
Variation Distance ◽  
The Right ◽  
Better Than

We present a method to obtain both exact values and sharp estimates for the total variation distance between binomial and Poisson distributions with the same mean λ. We give a simple efficient algorithm, whose complexity order is to compute exact values. Such an algorithm can be further simplified for moderate sample sizes n, provided that λ is neither close to from the left nor close to from the right. Sharp estimates, better than other known estimates in the literature, are also provided. The 0s of the second Krawtchouk and Charlier polynomials play a fundamental role.

scholarly journals ESTIMATION OF PARAMETERS FOR THE LIFETIME DISTRIBUTIONS

2019 ◽  
pp. 77-92
Author(s):  
Tabasam Sultana ◽  
Faqir Muhammad ◽  
Muhammad Aslam
Keyword(s):  
Least Squares ◽  
Method Of Moments ◽  
Goodness Of Fit ◽  
Mean Squared Error ◽  
Correlation Coefficients ◽  
Sample Sizes ◽  
Estimation Of Parameters ◽  
Lifetime Distributions ◽  
Squared Error ◽  
Probability Weighted Moments

This paper deals with various methods of estimation used for estimating the parameters of lifetime distributions. The distributions considered are exponential, Weibull, Rayleigh, lognormal and gamma and the method used are: method of moments, maximum likelihood, probability weighted moments, least squares and relative least squares. To compare the efficiency between the different methods of estimation, we used the total deviation, mean squared error and probability plot correlation coefficients. In order to study numerically, the execution of the different methods of estimation and goodness of fit analysis, their statistical properties have been simulated for different sample sizes. The graphs of bias designed for different methods of estimation have also been plotted against various sample sizes.  

scholarly journals Exact values and sharp estimates for the total variation distance between binomial and Poisson distributions

2008 ◽  
Vol 40 (04) ◽  
pp. 1033-1047
Author(s):  
José A. Adell ◽  
José M. Anoz ◽  
Alberto Lekuona
Keyword(s):  
Total Variation ◽  
Efficient Algorithm ◽  
Total Variation Distance ◽  
Sample Sizes ◽  
Charlier Polynomials ◽  
Sharp Estimates ◽  
Poisson Distributions ◽  
Variation Distance ◽  
The Right ◽  
Better Than

We present a method to obtain both exact values and sharp estimates for the total variation distance between binomial and Poisson distributions with the same mean λ. We give a simple efficient algorithm, whose complexity order is to compute exact values. Such an algorithm can be further simplified for moderate sample sizes n, provided that λ is neither close to from the left nor close to from the right. Sharp estimates, better than other known estimates in the literature, are also provided. The 0s of the second Krawtchouk and Charlier polynomials play a fundamental role.

Is Red Really Romantic?

2017 ◽  
Vol 48 (3) ◽  
pp. 174-183 ◽  
Author(s):  
Gabrielle K. Lehmann ◽  
Robert J. Calin-Jageman
Keyword(s):  
Opposite Direction ◽  
Positive Control ◽  
Weak Effect ◽  
Sample Sizes ◽  
Quality Controls

Abstract. Red has been reported to enhance attraction for women rating men ( Elliot et al., 2010 ) and men rating women ( Elliot & Niesta, 2008 ). We replicated one of these studies online and in-person. To ensure rigor, we obtained original materials, planned for informative sample sizes, pre-registered our study, used a positive control, and adopted quality controls. For men, we found a very weak effect in the predicted direction (d = 0.09, 95% CI [−0.17, 0.34], N = 242). For women, we found a very weak effect in the opposite direction (d = −0.09, 95% CI [−0.30, 0.12], N = 360). The original studies may have overestimated the red effect, our studies may be an underestimate, or there could be strong moderation of the effect of red on attraction.

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