Laplace Distribution Percent Point Calculator

Find the Laplace distribution percent point (quantile) x from a probability p and the location mu and scale b using the closed-form inverse.

Input

Enter a probability p with the location mu and scale b to get the Laplace distribution percent point (quantile) x using the closed-form inverse.

Probability p

Enter a value strictly between 0 and 1 (for example 0.95).

Probability type

Choose whether p is treated as a lower or an upper probability.

Location mu

The location parameter at the center of the distribution (any real number).

Scale b

The scale parameter, greater than zero (for example 1).

Percent point x for lower probability 0.95

2.30258509

Location mu

Scale b

Mean

Variance

Lower probability F(x)

0.95

Upper probability 1 minus F(x)

0.05

Density f(x)

0.05

Probability density function (PDF)

Cumulative distribution function (CDF)

The Laplace distribution has a location mu and a scale b greater than zero, with probability density f(x) equals (1 divided by 2b) times exp of minus the absolute value of x minus mu, divided by b.
Its cumulative distribution is F(x) equals 0.5 exp((x minus mu) divided by b) when x is below mu, and 1 minus 0.5 exp(minus (x minus mu) divided by b) when x is at least mu.
The percent point x for a lower probability p has a closed form: when p is below 0.5, x equals mu plus b times ln(2p); otherwise x equals mu minus b times ln(2 times (1 minus p)).
When you give an upper probability, it is converted to the lower probability 1 minus p and the same formula is applied.
The mean is mu, the variance is 2 b squared, and the standard deviation is the square root of 2 times b. Enter p strictly between 0 and 1.

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