Plot Distributions

Use the tool above to plot statistical distributions online that you can download as PDFs. The charts show the probability density (or mass) function and the cumulative distribution function. You can also generate and plot random samples from the distributions.

To get started, choose a distribution from the drop-down list and enter parameter values. For additional help click on the icon at the top right.

Supported distributions include:

  • Beta (Shape α, Shape β)
  • Binomial (Trials n, Probability p)
  • Cauchy (Location a, Scale γ)
  • Chi-squared (Degrees of freedom k)
  • Erlang (Shape k, Rate λ)
  • Exponential (Rate λ)
  • F (Degrees of freedom n, Degrees of freedom m)
  • Gamma (Shape k, Scale θ)
  • Laplace (Location μ, Scale s)
  • Levy (Location μ, Scale c)
  • Logarithmic (Probability p)
  • Logistic (Mean μ, Scale s)
  • Log-logistic (Shape α, Scale β)
  • Log-normal (Mean μ, Scale σ)
  • Negative binomial (Failures r, Probability of success p)
  • Normal (Mean μ, Scale σ)
  • Pareto (Scale k, Shape α)
  • Poisson (Rate λ)
  • Rayleigh (Scale σ)
  • Student's T (Degrees of freedom v)
  • Triangular (Maximum a, Minimum b, Mode c)
  • Uniform (Minimum a, Maximum b)
  • Weibull (Shape k, Scale λ)

Click on the "Details" button below the distribution selection to see full parameterization details for each distribution.

About

The charts are constructed using the d3 Javascript library. The underlying distributions are part of the Essy Distribution Javascript library.

Comments Leave a comment

  • Vanderlei Debastiani

    Amazing tool. Thank you!

    I think that the cumulative distribution function to Gamma is not right. The plot not make sense.

    Compare with R results:

    > dgamma(20, shape = 10, scale = 2)

    [1] 0.06255502

    > pgamma(20, shape = 10, scale = 2)

    [1] 0.5420703

    > qgamma(0.54, shape = 10, scale = 2)

    [1] 19.96693

  • Jack
    Thank you for the wonderful website. I am just wondering if you might add "Hypergeometric distribution"?
  • Dave
    Congrats guys. This is a very nice tool. I wish all the applications you can find round there couls be as useful as this one.
  • Farid
    Little issue when plotting the chi-squared distribution with 3 degrees of freedom and x = 10, for the CDF the result is: P(X≤10) = 1.10743 which is impossible (a probability can't be more than 1)
  • alexbottoni
    Absolutely amazing tool. Very useful for studying distributions and for evaluating effects of parameters. Congratulation!
  • Sam
    Thank you, this is just the tool I was looking for!
  • Jess
    For Lognormal distribution, mean and standard deviation are from ln(x)?
  • Guerschom
    Great help. Is it possible to draw 2 distributions on the same graph ?
    • EssyCodeModerator
      You can plot multiple distributions of the same type using the push-pin icon above and to the right of the charts -- but not distributions of different types at this point.
  • Brian
    Nice tool! But for some reason I can't get gamma distribution for k (shape factor) < 1
    • EssyCodeModerator
      Good point, doesn't work for me either. I will check it out.
  • Neel
    Thank you
  • Ahmad

    Very nice and great help.

    I'm wondering if you can add Dirichlet distribution?

    • EssyCodeModerator
      Thanks for the suggestion, I will look into it.
  • anonymous
    Thank you very for such wonderful tool. It would be nice if we can plot two or more plots simultaneously. Thanks
    • EssyCodeModerator
      Did you see the "pin" function? There's a thumbtack icon that appears in the upper-right once you've plotted a distribution. This will let you display multiple plots of the same distribution type; if you mean plotting different distribution types at the same time that would be a challenge but IMore can put it on my list. Thanks for the comment.
  • Erik
    Thank you so much, helped me understand the impact of the distribution parameters!
  • Kevin
    Very useful website for my students!

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