Convergence of binomial to normal: multiple proofs

  title={Convergence of binomial to normal: multiple proofs},
  author={Subhash C. Bagui and K. L. Mehra},
This article presents four different proofs of the convergence of the Binomial ( , ) B n p distribution to a limiting normal distribution, n. These contrasting proofs may not be all found together in a single book or an article in the statistical literature. Readers of this article would find the presentation informative and especially useful from the pedagogical standpoint. This review of proofs should be of interest to teachers and students of senior undergraduate courses in probability and… 
On the asymptotic behavior of the $q$-analog of Kostant's partition function
Kostant's partition function counts the number of distinct ways to express a weight of a classical Lie algebra $\mathfrak{g}$ as a sum of positive roots of $\mathfrak{g}$. We refer to each of these
How to reuse existing annotated image quality datasets to enlarge available training data with new distortion types
Results of the subjective experiments indicate that it may be possible to use information gained from older datasets to describe the perceived quality of more recent compression algorithms.
Machine Learning for Sparse Time-Series Classification - An Application in Smart Metering
Smart Meters are measuring devices collecting labeled time series data of utility consumptions from sub-meters and are capable of automatically transmit-ting this between the customer and utility c


Convergence of Binomial, Poisson, Negative-Binomial, and Gamma to Normal Distribution: Moment Generating Functions Technique
In this article, we employ moment generating functions (mgf’s) of Binomial, Poisson, Negative-binomial and gamma distributions to demonstrate their convergence to normality as one of their parameters
The Normal Approximation to the Binomial
This note presents a heuristic derivation of the central limit theorem for Bernoulli random variables. While not a proof, it lends insight into why the normal distribution approximates the binomial
Introduction to Probability and Mathematical Statistics
Probability Random Variables and Their Distributions Special Probability Distributions Joint Distributions Properties of Random Variables Functions of Random Variables Limiting Distributions
Nonrigorous Proofs of Stirling's Formula
(ProQuest: ... denotes formulae omitted.)1. INTRODUCTIONWe present a method of deriving Stirling's formula together with two existing methods. The new method uses a result on convergence of moments
An Introduction To Probability Theory And Its Applications
A First Course in Probability (8th ed.) by S. Ross is a lively text that covers the basic ideas of probability theory including those needed in statistics.
  • Grey Giddins
  • History
    The Journal of hand surgery, European volume
  • 2016
Muteism is often manifest in several members of a family derived from a com'mon, though not a deaf-and-dumb stock, and is more common in the rural than in the civic portions; and in the hilly than the flat districts.
Elementary statistics, in a world of applications
Methodus Differentialis, London, 1730
  • Received: February
  • 2017
Convergence of binomial
  • Poisson, negativebinomial, and gamma to normal distribution: Moment generating functions technique, American Journal of Mathematics and Statistics, 6
  • 2016