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Distribution of quadratic form n(xbar-mu)Sigma(xbar-mu), where x~MVN(mu,sigma)
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Classroom Contents
Characteristic, Moment Generating, Factorial Generating Functions
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- 1 Inequality for Absolute Value of Expected Value
- 2 Derivatives of a Characteristic Function are Bounded
- 3 Properties of the Characteristic Function (part 1)
- 4 Properties of the Characteristic Function (part 2)
- 5 Inversion Formula for a Characteristic Function (part 1)
- 6 Inversion Formula (part 2)
- 7 Inversion Formula Example (part 3)
- 8 Properties of the Moment Generating Function (part 1)
- 9 Properties of the Moment Generating Function (part 2)
- 10 Factorial Moment Generating Function. Probability Generating Function.
- 11 Joint Characteristic Function
- 12 Generating Functions for Gamma Distribution
- 13 Generating Functions for Poisson Distribution
- 14 Generating Functions for Normal Distribution
- 15 Generating Functions for Binomial Distribution
- 16 Generating Functions for Multinomial Distribution
- 17 Generating Functions for Cauchy Distribution
- 18 Some Applications of Characteristic Functions
- 19 Illustration using univariate LOTUS: Derive the MGF for a 1 df noncentral Chi square Distribution
- 20 Illustration using multivariate LOTUS: Derive the MGF or a k df noncentral Chi square Distribution
- 21 Distribution of quadratic form n(xbar-mu)Sigma(xbar-mu), where x~MVN(mu,sigma)
- 22 Mean, Variance, MGF, & CDF of a Gumbel Distribution
- 23 Distribution for the Sum of Negative Binomial Random Variables Using the MGF
- 24 Derive the MGF of a Logistic Distribution and use it to derive the Mean and Variance
