stats

Exponential Distribution

Exponential distribution — PDF, CDF, survival function S(x), hazard rate, memoryless property explainer; λ or mean input.

Parameters

Input as

Rate λ (> 0)

mean = 1

Presets

Calculation

x value (≥ 0)

P(a < X < b) — lower a

P(a < X < b) — upper b (> a)

Results

PDF (green, left axis: 0..λ)CDF (violet, right axis: 0..1)amber line = x

PDF f(x) = λe^−λx0.3679

CDF F(x) = 1 − e^−λx0.6321

Survival S(x) = e^−λx0.3679

P(X > x)0.3679

Hazard rate h(x) = λ1

P(0.5 < X < 2)0.4712

Distribution properties

Mean 1/λ1

Median ln(2)/λ0.6931

Std dev 1/λ1

Variance 1/λ²1

Skewness2

CV (σ/μ)1

Mode0

f(x) = λe^−λx · F(x) = 1−e^−λx · S(x) = e^−λx · h(x) = λ