Probability Distribution Calculator

Probability Distribution Calculator

Calculates one probability for three selectable distributions: normal cumulative P(X<=threshold), Poisson point probability P(X=k), or binomial point probability P(X=k). The shared fields mean mu/lambda/n for parameter1, sigma/k/p for parameter2, and the third field is the threshold for normal or k for binomial; Poisson uses parameter2 as k and ignores the third field.

Normal mode requires a finite mean, a standard deviation greater than zero and a finite threshold. It evaluates Phi((threshold-mu)/sigma) using an error-function approximation. Verified standard normal input mu0,sigma1,threshold0 returns0.50000000. It is a CDF, not a density, interval probability, inverse quantile or random sampler.

Poisson mode requires finite lambda>=0 and integer k from 0 through 100000. It evaluates exp(-lambda+k*ln(lambda)-ln(k!)) using a summed log-factorial to avoid direct factorial overflow. Verified lambda2,k3 returns0.18044704; lambda0,k0 returns1 and lambda0 with positive k returns0.

Binomial mode requires integer n from 0 through 100000, finite p from 0 through 1 and integer k from 0 through n. It evaluates exp(ln(n!)-ln(k!)-ln((n-k)!)+k*ln(p)+(n-k)*ln(1-p)), with exact endpoint handling for p=0 and p=1. Verified n10,p0.5,k3 returns0.11718750; n0,p0,k0 returns1.

Results show eight fractional digits and follow the page locale's number formatting when available. Use a decimal point, as in 0.5, without thousands separators or lists. Comma input depends on the browser and is not guaranteed. Check the field value before calculating. Extremely small probabilities can round to 0.00000000; this does not prove that the mathematical probability is exactly zero.

Calculation runs locally in the browser without server or AI calls. This calculator does not estimate parameters, fit data, compute confidence intervals, validate a statistical model or provide medical/financial conclusions. Choose the distribution, map each field carefully, calculate, and verify the assumptions before using the result in consequential work.