Continuous Probability Distributions

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Cauchy Distribution

1.  A random variable (rv) X has a general Cauchy distribution with parametersμ and&la...}
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Characteristics Function of Cauchy Distribution

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Characteristic Function Of Cauchy Distribution

1. Then the characteristic function of Cauchy distribution X is given by

   Φ_...}

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Gamma Distribution

1. $$ \Gamma(1) \ = \ \int_{0}^{\infty} \ {e^-}^{x} \ dx \ = \ 1$$

2. $$ \G...}

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Moment Generating Function of Gamma Distribution, Harmonic Mean and Mode of Gamma Distribution

1. The mean and variance of a Gamma distribution is α
2. The mode of the gamma dis...}
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Beta Distribution

1. Beta distribution is one of the two parameters continuous probability distribution. A c...}

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Mode of Beta Distribution of First kind and Beta Distribution of Second Kind

1. The mode of the beta distribution of first kind with parameters m and n is

   $$x =...}

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Negative Exponential Distribution

1. A random variable (rv) X having a probability density function (pdf) :

   $$f(x) \...}

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Interquartile Range, Mean Deviation about Mean and fitting of of Negative Exponential Distribution and Laplace Distribution

Uses of Negative Exponential Distribution

1.  Exponential Distribution

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Moments and Moment Generating Function of Standard Laplace Distribution

1. The standard Laplace distribution is symmetrical but it is leptokurtic.
2.  The...}
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Logistic Distribution and Properties of Negative Exponential Distribution

• Mean of Logistic distribution isα but standard Logistic distribution has zero mean.
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Weibull Distribution

1. This distribution was used to study experimentally the breaking strength and elasticity of...}
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Log-Normal Distribution

1. The moment coefficient of skewness is given by

   $$\gamma_1 \ = \ ({e^\sigma}^{2}...}

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