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Exponential Distribution Percent Point Calculator

Find the percent point (quantile) x of an exponential distribution from a probability p and rate lambda using the closed form. Supports lower and upper tail probabilities and shows mean, variance, and PDF and CDF charts.

Input

Enter a probability p and rate parameter lambda to find the percent point (quantile) x of the exponential distribution. Both lower and upper tail probabilities are supported.

A value greater than 0 and less than 1

Probability mode

Whether p is a lower or upper tail probability

A positive value. The mean equals 1/lambda

Result

Percent point x for lower probability 0.95

2.99573227

Rate lambda

1

Mean 1/lambda

1

Lower probability F(x)

0.95

Upper probability 1-F(x)

0.05

Density f(x)

0.05

Variance 1/lambda squared

1

Probability density function PDF

Cumulative distribution function CDF

How it works

  • The cumulative distribution of the exponential distribution is F(x) = 1 - e^(-lambda x) for x at least 0.
  • For a lower tail probability p, the percent point is x = -ln(1 - p) / lambda.
  • For an upper tail probability p, the percent point is x = -ln(p) / lambda.
  • The mean is 1/lambda and the variance is 1/lambda squared. The density is f(x) = lambda e^(-lambda x).
  • Enter a probability p between 0 and 1 (exclusive) and a positive rate lambda.

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