Improved approximate confidence intervals for the mean of a log-normal random variable

2002 ◽  
Vol 21 (10) ◽  
pp. 1443-1459 ◽  
Author(s):  
Douglas J. Taylor ◽  
Lawrence L. Kupper ◽  
Keith E. Muller
Keyword(s):  
Confidence Intervals ◽  
Random Variable ◽  
Normal Random Variable ◽  
The Mean ◽  
Approximate Confidence Intervals ◽  
Log Normal

scholarly journals Assessing the Accuracy of Approximate Confidence Intervals Proposed for the Mean of Poisson Distribution

2020 ◽  
Vol 18 (1) ◽  
pp. 2-13
Author(s):  
Alireza Shirvani ◽  
Malek Fathizadeh
Keyword(s):  
Confidence Interval ◽  
Confidence Intervals ◽  
Poisson Distribution ◽  
Count Data ◽  
Coverage Probability ◽  
Discrete Distribution ◽  
Interval Length ◽  
Average Confidence ◽  
The Mean ◽  
Approximate Confidence Intervals

The Poisson distribution is applied as an appropriate standard model to analyze count data. Because this distribution is known as a discrete distribution, representation of accurate confidence intervals for its distribution mean is extremely difficult. Approximate confidence intervals were presented for the Poisson distribution mean. The purpose of this study is to simultaneously compare several confidence intervals presented, according to the average coverage probability and accurate confidence coefficient and the average confidence interval length criteria.

Prediction Intervals and Empirical Bayes Confidence Intervals

1975 ◽  
Vol 12 (S1) ◽  
pp. 47-55 ◽  
Author(s):  
D. R. Cox
Keyword(s):  
Confidence Intervals ◽  
Empirical Bayes ◽  
Random Variable ◽  
Bayes Estimation ◽  
Prediction Intervals ◽  
Empirical Bayes Estimation ◽  
Approximate Confidence Intervals

Approximate parametric prediction intervals are obtained for an unobserved random variable when the amount of data on which to base the estimation is large. Applications include the construction of approximate confidence intervals in empirical Bayes estimation.

Generation of Correlated Logistic-Normal Random Variates for Medical Decision Trees

1998 ◽  
Vol 37 (03) ◽  
pp. 235-238 ◽  
Author(s):  
M. El-Taha ◽  
D. E. Clark
Keyword(s):  
Monte Carlo ◽  
Decision Trees ◽  
Computer Algebra ◽  
Taylor Series ◽  
Computer Algebra System ◽  
Random Variable ◽  
Monte Carlo Analysis ◽  
Normal Random Variable ◽  
Medical Decision ◽  
Theoretical Results

AbstractA Logistic-Normal random variable (Y) is obtained from a Normal random variable (X) by the relation Y = (ex)/(1 + ex). In Monte-Carlo analysis of decision trees, Logistic-Normal random variates may be used to model the branching probabilities. In some cases, the probabilities to be modeled may not be independent, and a method for generating correlated Logistic-Normal random variates would be useful. A technique for generating correlated Normal random variates has been previously described. Using Taylor Series approximations and the algebraic definitions of variance and covariance, we describe methods for estimating the means, variances, and covariances of Normal random variates which, after translation using the above formula, will result in Logistic-Normal random variates having approximately the desired means, variances, and covariances. Multiple simulations of the method using the Mathematica computer algebra system show satisfactory agreement with the theoretical results.

scholarly journals Random additions in urns of integers

2021 ◽  
Vol 58 (2) ◽  
pp. 335-346
Author(s):  
Mackenzie Simper
Keyword(s):  
Finite Group ◽  
Random Process ◽  
Uniform Distribution ◽  
Discrete Time ◽  
Random Variable ◽  
Urn Model ◽  
Infinite Type ◽  
The Mean ◽  
A Finite Group ◽  
Proof Of Convergence

AbstractConsider an urn containing balls labeled with integer values. Define a discrete-time random process by drawing two balls, one at a time and with replacement, and noting the labels. Add a new ball labeled with the sum of the two drawn labels. This model was introduced by Siegmund and Yakir (2005) Ann. Prob.33, 2036 for labels taking values in a finite group, in which case the distribution defined by the urn converges to the uniform distribution on the group. For the urn of integers, the main result of this paper is an exponential limit law. The mean of the exponential is a random variable with distribution depending on the starting configuration. This is a novel urn model which combines multi-drawing and an infinite type of balls. The proof of convergence uses the contraction method for recursive distributional equations.

Visualizing the Variance of a Random Variable

2011 ◽  
Vol 18 (01) ◽  
pp. 71-85
Author(s):  
Fabrizio Cacciafesta
Keyword(s):  
Stochastic Dominance ◽  
Mean Absolute Error ◽  
Random Variable ◽  
Absolute Error ◽  
Second Order ◽  
Taylor Formula ◽  
Order Stochastic Dominance ◽  
The Mean ◽  
Second Order Stochastic Dominance ◽  
Options Theory

We provide a simple way to visualize the variance and the mean absolute error of a random variable with finite mean. Some application to options theory and to second order stochastic dominance is given: we show, among other, that the "call-put parity" may be seen as a Taylor formula.

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