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Probability Density Function | The general formula for the probability density function of the double exponential distribution is![]() where ![]() ![]() ![]() ![]() ![]() Since the general form of probability functions can be expressed in terms of the standard distribution, all subsequent formulas in this section are given for the standard form of the function. The following is the plot of the double exponential probability density function. ![]() | ||||||||||||||||
Cumulative Distribution Function | The formula for the cumulative distribution function of the double exponential distribution is![]() The following is the plot of the double exponential cumulative distribution function. ![]() | ||||||||||||||||
Percent Point Function | The formula for the percent point function of the double exponential distribution is![]() The following is the plot of the double exponential percent point function. ![]() | ||||||||||||||||
Hazard Function | The formula for the hazard function of the double exponential distribution is![]() The following is the plot of the double exponential hazard function. ![]() | ||||||||||||||||
Cumulative Hazard Function | The formula for the cumulative hazard function of the double exponential distribution is![]() The following is the plot of the double exponential cumulative hazard function. ![]() | ||||||||||||||||
Survival Function | The double exponential survival function can be computed from the cumulative distribution function of the double exponential distribution.The following is the plot of the double exponential survival function.![]() | ||||||||||||||||
Inverse Survival Function | The formula for the inverse survival function of the double exponential distribution is![]() The following is the plot of the double exponential inverse survival function. ![]() | ||||||||||||||||
Common Statistics |
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Parameter Estimation | The maximum likelihood estimators of the location and scale parameters of the double exponential distribution are![]() ![]() where ![]() | ||||||||||||||||
Software | Some general purpose statistical software programs support at least some of the probability functions for the double exponential distribution. |
Weibull Distribution Probability Density Function The formula for the probability density function of the general Weibull distribution is where is the shape parameter , is the location parameter and is the scale parameter . The case where = 0 and = 1 is called the standard Weibull distribution . The case where = 0 is called the 2-parameter Weibull distribution. The equation for the standard Weibull distribution reduces to Since the general form of probability functions can be expressed in terms of the standard distribution , all subsequent formulas in this section are given for the standard form of the function. The following is the plot of the Weibull probability density function. Cumulative Distribution Function The formula for the cumulative distribution function of the Weibull distribution is The following is the plot of the Weibull cumulative ...
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