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probFunCal2

A Web-Based Calculator For Calculating Probability Distribution Functions As Binomial, Poisson, Exponential, Gamma, Beta, Uniform, Weibull, Lognormal, Cauchy, Geometric, And Negative Binomial Distributions

By W. J. Zhang



The user manual guide and suggested citation of this page:
Zhang W. J. 2026. probFunCal2: A web-based calculator for calculating probability distribution functions as binomial, Poisson, exponential, gamma, beta, uniform, Weibull, lognormal, Cauchy, geometric, and negative binomial distributions. Selforganizology, 13(3-4): 26-65
Also, click here to download the corresponding offline calculator.


Binomial Distribution
Number of trials (n):

Number of successes (k):

Probability of success (p):



Probability mass f(k):
Number of trials (n):

Number of successes (k):

Probability of success (p):



Cumulative probability F(k):
Probability (p):

Number of trials (n):

Probability of success (prob):



Quantile (k):


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Poisson Distribution
Number of events (k):

Rate parameter (λ):



Probability mass f(k):
Number of events (k):

Rate parameter (λ):



Cumulative probability F(k):
Probability (p):

Rate parameter (λ):



Quantile (k):


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Exponential Distribution
Random variable (x):

Rate parameter (λ):



Probability density f(x):
Random variable (x):

Rate parameter (λ):



Cumulative probability F(x):
Probability (p):

Rate parameter (λ):



Quantile (x):


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Gamma Distribution
Random variable (x):

Shape parameter (α):

Scale parameter (β):



Probability density f(x):
Random variable (x):

Shape parameter (α):

Scale parameter (β):



Cumulative probability F(x):
Probability (p):

Shape parameter (α):

Scale parameter (β):



Quantile (x):


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Beta Distribution
Random variable (x):

Shape parameter α:

Shape parameter β:



Probability density f(x):
Random variable (x):

Shape parameter α:

Shape parameter β:



Cumulative probability F(x):
Probability (p):

Shape parameter α:

Shape parameter β:



Quantile (x):


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Uniform Distribution
Random variable (x):

Lower bound (a):

Upper bound (b):



Probability density f(x):
Random variable (x):

Lower bound (a):

Upper bound (b):



Cumulative probability F(x):
Probability (p):

Lower bound (a):

Upper bound (b):



Quantile (x):


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Weibull Distribution
Random variable (x):

Shape parameter (k):

Scale parameter (λ):



Probability density f(x):
Random variable (x):

Shape parameter (k):

Scale parameter (λ):



Cumulative probability F(x):
Probability (p):

Shape parameter (k):

Scale parameter (λ):



Quantile (x):


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Lognormal Distribution
Random variable (x):

Location parameter (μ):

Scale parameter (σ):



Probability density f(x):
Random variable (x):

Location parameter (μ):

Scale parameter (σ):



Cumulative probability F(x):
Probability (p):

Location parameter (μ):

Scale parameter (σ):



Quantile (x):


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Cauchy Distribution
Random variable (x):

Location parameter (x₀):

Scale parameter (γ):



Probability density f(x):
Random variable (x):

Location parameter (x₀):

Scale parameter (γ):



Cumulative probability F(x):
Probability (p):

Location parameter (x₀):

Scale parameter (γ):



Quantile (x):


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Geometric Distribution
Number of failures (k):

Probability of success (p):



Probability mass f(k):
Number of failures (k):

Probability of success (p):



Cumulative probability F(k):
Probability (p):

Probability of success (prob):



Quantile (k):


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Negative Binomial Distribution
Number of failures (k):

Number of successes (r):

Probability of success (p):



Probability mass f(k):
Number of failures (k):

Number of successes (r):

Probability of success (p):



Cumulative probability F(k):
Probability (p):

Number of successes (r):

Probability of success (prob):



Quantile (k):


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User manual guide:
Zhang W. J. 2026. probFunCal2: A web-based calculator for calculating probability distribution functions as binomial, Poisson, exponential, gamma, beta, uniform, Weibull, lognormal, Cauchy, geometric, and negative binomial distributions. Selforganizology, 13(3-4): 26-65

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