Mathematical Statistics Estimators of Parameters Ex: Method of Moments for a Gamma Distribution

Applied Statistics Class 7 Spring 2022.
A statistic is a function of a random sample which is a list of n independent random variables from the same population distribution.
The sample mean and sample variance are prominent examples which are unbiased point estimators for the population mean and variance.
The method of moments is used to find point estimators for the parameters α and β of a Gamma Distribution.
This is used to model the Chutes and Ladders game.
Probability and Statistics with Applications: A Problem Solving Text by Asimow and Maxwell probability statistics mathematicalstatistics Links and resources ? Subscribe to Bill Kinney Math: ? Subscribe to my Math Blog Infinity is Really Big: ? Follow me on Twitter: ? Follow me on Instagram: ? You can support me by buying Infinite Powers How Calculus Reveals the Secrets of the Universe by Steven Strogatz or anything else you want to buy starting from this link: ? Check out my artist son Tyler Kinneys website: 0:00 Applied statistics should be grounded in theoretical mathematical statistics 0:45 Chutes and Ladders Mathematica simulation 5:26 Ultimate goal: relate this to a Gamma distribution 7:26 Want to make the graph of the PDF match the histogram 11:21 Populations and samples both practically and theoretically 13:42 Population and random sample of random variables independent and identically distributed random variables 15:59 Joint PDF of X1X2...Xn is the product of n values of the PDF of X 19:38 Parameters for the population such as mean and median 24:06 Statistics based on the random sample as random variables 26:19 Sample mean statistic estimator of the population mean μ 27:35 Sample variance estimator of population variance σ2 29:21 S2 is an unbiased estimator for σ2 30:34 X bar is an unbiased estimator for μ 35:40 Proof that ES2σ2 is in the appendix 38:02 Variance of the sample mean: VarX bar 43:16 Target practice analogy 46:06 The sample mean is a consistent estimator for the population mean μ 47:44 An estimator is a statistic which is a random variable based on a random sample of independent random variables from the same distribution 48:48 Back to the Gamma distribution example Chutes and Ladders simulation 50:31 EXαβ and VarXαβ2 51:49 Can find estimators for α and β 52:26 Method of Moments estimators for α and β parameters of a Gamma distribution 57:23 Solve the system of nonlinear equations 59:17 Replace α and β with their estimators 1:00:31 Observed values estimates for Chutes and Ladders simulation 1:02:02 Observed value m2 of logical estimator for second moment EX2 1:04:47 Observed estimates of α and β 1:07:23 Other topics in mathematical statistics AMAZON ASSOCIATE As an Amazon Associate I earn from qualifying purchases.

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