Gamma Distribution Percent Point
Find the percent point (quantile) x of the gamma distribution from probability p, tail, shape k, and scale theta using the inverse regularized incomplete gamma. Lower and upper tails supported.
Input
Compute the percent point (quantile, inverse CDF) of the gamma distribution. Enter the probability, tail, shape k, and scale theta.
A probability between 0 and 1 (e.g. 0.95)
Whether p refers to the lower or upper tail probability
A real number greater than 0
A real number greater than 0
Result
Percent point x for p = 0.95 (Lower tail F(x) = p)
4.74386452
Shape k
2
Scale theta
1
Lower probability F(x)
0.95
Upper probability 1 minus F(x)
0.05
Density f(x)
0.04129506
Mean
2
Variance
2
Probability density function PDF
Cumulative distribution function CDF
How it works
- The density is f(x) = x^(k-1) e^(-x/theta) / (theta^k Gamma(k)) and the cumulative distribution is F(x) = P(k, x/theta), the regularized lower incomplete gamma.
- The lower percent point is the x with F(x) = p, while the upper percent point is the x with 1 minus F(x) = p, that is F(x) = 1 minus p.
- The inverse x is obtained by solving P(k, z) = target probability for the standardized variable z = x/theta. The tool combines Newton iteration with bisection for high accuracy.
- The mean is k times theta, the variance is k times theta squared, and the standard deviation is its square root.
- k is the shape parameter (greater than 0), theta is the scale parameter (greater than 0), and p is a probability between 0 and 1.
Reviews
Tell us what you think of this calculator.
Write a review
- Home
Gamma Distribution Percent Point