Probability Density Function and Laplace Distribution

A random variable has a Laplace distribution (µ, b) if it has a probability density function. Say (µ) is a location parameter and b> 0, which is referred as diversity, is a scale parameter.
If (µ) = 0 and b =1 the positive half line is an exactly exponential distribution scale by ½. The probability density function of Laplace distribution is also reminiscent of the normal distribution, however, the Normal distribution is expressed in the term of the square difference of the mean (µ), and the Laplace distribution density is expressed in term of absolute difference from mean. Consequently, the Laplace distribution has a fatter tail than the mean distribution.

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