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As an instance of the [`rv_continuous`](https://docs.scipy.org/doc/scipy-1.15.2/reference/generated/scipy.stats.rv_continuous.html#scipy.stats.rv_continuous "scipy.stats.rv_continuous") class, [`beta`](https://docs.scipy.org/doc/scipy-1.15.2/reference/generated/scipy.stats.beta.html#scipy.stats.beta "scipy.stats.beta") object inherits from it a collection of generic methods (see below for the full list), and completes them with details specific for this particular distribution. Notes The probability density function for [`beta`](https://docs.scipy.org/doc/scipy-1.15.2/reference/generated/scipy.stats.beta.html#scipy.stats.beta "scipy.stats.beta") is: \\\[f(x, a, b) = \\frac{\\Gamma(a+b) x^{a-1} (1-x)^{b-1}} {\\Gamma(a) \\Gamma(b)}\\\] for \\(0 \<= x \<= 1\\), \\(a \> 0\\), \\(b \> 0\\), where \\(\\Gamma\\) is the gamma function ([`scipy.special.gamma`](https://docs.scipy.org/doc/scipy-1.15.2/reference/generated/scipy.special.gamma.html#scipy.special.gamma "scipy.special.gamma")). [`beta`](https://docs.scipy.org/doc/scipy-1.15.2/reference/generated/scipy.stats.beta.html#scipy.stats.beta "scipy.stats.beta") takes \\(a\\) and \\(b\\) as shape parameters. This distribution uses routines from the Boost Math C++ library for the computation of the `pdf`, `cdf`, `ppf`, `sf` and `isf` methods. [\[1\]](https://docs.scipy.org/doc/scipy-1.15.2/reference/generated/scipy.stats.beta.html#r8b11f181b37f-1) The probability density above is defined in the “standardized” form. To shift and/or scale the distribution use the `loc` and `scale` parameters. Specifically, `beta.pdf(x, a, b, loc, scale)` is identically equivalent to `beta.pdf(y, a, b) / scale` with `y = (x - loc) / scale`. Note that shifting the location of a distribution does not make it a “noncentral” distribution; noncentral generalizations of some distributions are available in separate classes. References \[[1](https://docs.scipy.org/doc/scipy-1.15.2/reference/generated/scipy.stats.beta.html#id1)\] The Boost Developers. “Boost C++ Libraries”. <https://www.boost.org/>. Examples Try it in your browser\! ``` >>> import numpy as np >>> from scipy.stats import beta >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(1, 1) ``` Calculate the first four moments: ``` >>> a, b = 2.31, 0.627 >>> mean, var, skew, kurt = beta.stats(a, b, moments='mvsk') ``` Display the probability density function (`pdf`): ``` >>> x = np.linspace(beta.ppf(0.01, a, b), ... beta.ppf(0.99, a, b), 100) >>> ax.plot(x, beta.pdf(x, a, b), ... 'r-', lw=5, alpha=0.6, label='beta pdf') ``` Alternatively, the distribution object can be called (as a function) to fix the shape, location and scale parameters. This returns a “frozen” RV object holding the given parameters fixed. Freeze the distribution and display the frozen `pdf`: ``` >>> rv = beta(a, b) >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf') ``` Check accuracy of `cdf` and `ppf`: ``` >>> vals = beta.ppf([0.001, 0.5, 0.999], a, b) >>> np.allclose([0.001, 0.5, 0.999], beta.cdf(vals, a, b)) True ``` Generate random numbers: ``` >>> r = beta.rvs(a, b, size=1000) ``` And compare the histogram: ``` >>> ax.hist(r, density=True, bins='auto', histtype='stepfilled', alpha=0.2) >>> ax.set_xlim([x[0], x[-1]]) >>> ax.legend(loc='best', frameon=False) >>> plt.show() ```  Go Back Open In Tab Methods | | | |---|---| | **rvs(a, b, loc=0, scale=1, size=1, random\_state=None)** | Random variates. | | **pdf(x, a, b, loc=0, scale=1)** | Probability density function. | | **logpdf(x, a, b, loc=0, scale=1)** | Log of the probability density function. | | **cdf(x, a, b, loc=0, scale=1)** | Cumulative distribution function. | | **logcdf(x, a, b, loc=0, scale=1)** | Log of the cumulative distribution function. | | **sf(x, a, b, loc=0, scale=1)** | Survival function (also defined as `1 - cdf`, but *sf* is sometimes more accurate). | | **logsf(x, a, b, loc=0, scale=1)** | Log of the survival function. | | **ppf(q, a, b, loc=0, scale=1)** | Percent point function (inverse of `cdf` — percentiles). | | **isf(q, a, b, loc=0, scale=1)** | Inverse survival function (inverse of `sf`). | | **moment(order, a, b, loc=0, scale=1)** | Non-central moment of the specified order. | | **stats(a, b, loc=0, scale=1, moments=’mv’)** | Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’). | | **entropy(a, b, loc=0, scale=1)** | (Differential) entropy of the RV. | | **fit(data)** | Parameter estimates for generic data. See [scipy.stats.rv\_continuous.fit](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_continuous.fit.html#scipy.stats.rv_continuous.fit) for detailed documentation of the keyword arguments. | | **expect(func, args=(a, b), loc=0, scale=1, lb=None, ub=None, conditional=False, \*\*kwds)** | Expected value of a function (of one argument) with respect to the distribution. | | **median(a, b, loc=0, scale=1)** | Median of the distribution. | | **mean(a, b, loc=0, scale=1)** | Mean of the distribution. | | **var(a, b, loc=0, scale=1)** | Variance of the distribution. | | **std(a, b, loc=0, scale=1)** | Standard deviation of the distribution. | | **interval(confidence, a, b, loc=0, scale=1)** | Confidence interval with equal areas around the median. | [previous scipy.stats.argus](https://docs.scipy.org/doc/scipy-1.15.2/reference/generated/scipy.stats.argus.html "previous page") [next scipy.stats.betaprime](https://docs.scipy.org/doc/scipy-1.15.2/reference/generated/scipy.stats.betaprime.html "next page") On this page - [`beta`](https://docs.scipy.org/doc/scipy-1.15.2/reference/generated/scipy.stats.beta.html#scipy.stats.beta) © Copyright 2008-2025, The SciPy community. Created using [Sphinx](https://www.sphinx-doc.org/) 7.3.7. Built with the [PyData Sphinx Theme](https://pydata-sphinx-theme.readthedocs.io/en/stable/index.html) 0.15.2.

scipy.stats.beta *\= \<scipy.stats.\_continuous\_distns.beta\_gen object\>*[\[source\]](https://github.com/scipy/scipy/blob/v1.15.2/scipy/stats/_continuous_distns.py#L0-L1)[\#](https://docs.scipy.org/doc/scipy-1.15.2/reference/generated/scipy.stats.beta.html#scipy.stats.beta "Link to this definition") A beta continuous random variable. As an instance of the [`rv_continuous`](https://docs.scipy.org/doc/scipy-1.15.2/reference/generated/scipy.stats.rv_continuous.html#scipy.stats.rv_continuous "scipy.stats.rv_continuous") class, [`beta`](https://docs.scipy.org/doc/scipy-1.15.2/reference/generated/scipy.stats.beta.html#scipy.stats.beta "scipy.stats.beta") object inherits from it a collection of generic methods (see below for the full list), and completes them with details specific for this particular distribution. Notes The probability density function for [`beta`](https://docs.scipy.org/doc/scipy-1.15.2/reference/generated/scipy.stats.beta.html#scipy.stats.beta "scipy.stats.beta") is: \\\[f(x, a, b) = \\frac{\\Gamma(a+b) x^{a-1} (1-x)^{b-1}} {\\Gamma(a) \\Gamma(b)}\\\] for \\(0 \<= x \<= 1\\), \\(a \> 0\\), \\(b \> 0\\), where \\(\\Gamma\\) is the gamma function ([`scipy.special.gamma`](https://docs.scipy.org/doc/scipy-1.15.2/reference/generated/scipy.special.gamma.html#scipy.special.gamma "scipy.special.gamma")). [`beta`](https://docs.scipy.org/doc/scipy-1.15.2/reference/generated/scipy.stats.beta.html#scipy.stats.beta "scipy.stats.beta") takes \\(a\\) and \\(b\\) as shape parameters. This distribution uses routines from the Boost Math C++ library for the computation of the `pdf`, `cdf`, `ppf`, `sf` and `isf` methods. [\[1\]](https://docs.scipy.org/doc/scipy-1.15.2/reference/generated/scipy.stats.beta.html#r8b11f181b37f-1) The probability density above is defined in the “standardized” form. To shift and/or scale the distribution use the `loc` and `scale` parameters. Specifically, `beta.pdf(x, a, b, loc, scale)` is identically equivalent to `beta.pdf(y, a, b) / scale` with `y = (x - loc) / scale`. Note that shifting the location of a distribution does not make it a “noncentral” distribution; noncentral generalizations of some distributions are available in separate classes. References Examples ``` >>> import numpy as np >>> from scipy.stats import beta >>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots(1, 1) ``` Calculate the first four moments: ``` >>> a, b = 2.31, 0.627 >>> mean, var, skew, kurt = beta.stats(a, b, moments='mvsk') ``` Display the probability density function (`pdf`): ``` >>> x = np.linspace(beta.ppf(0.01, a, b), ... beta.ppf(0.99, a, b), 100) >>> ax.plot(x, beta.pdf(x, a, b), ... 'r-', lw=5, alpha=0.6, label='beta pdf') ``` Alternatively, the distribution object can be called (as a function) to fix the shape, location and scale parameters. This returns a “frozen” RV object holding the given parameters fixed. Freeze the distribution and display the frozen `pdf`: ``` >>> rv = beta(a, b) >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf') ``` Check accuracy of `cdf` and `ppf`: ``` >>> vals = beta.ppf([0.001, 0.5, 0.999], a, b) >>> np.allclose([0.001, 0.5, 0.999], beta.cdf(vals, a, b)) True ``` Generate random numbers: ``` >>> r = beta.rvs(a, b, size=1000) ``` And compare the histogram: ``` >>> ax.hist(r, density=True, bins='auto', histtype='stepfilled', alpha=0.2) >>> ax.set_xlim([x[0], x[-1]]) >>> ax.legend(loc='best', frameon=False) >>> plt.show() ```  Methods | | | |---|---| | **rvs(a, b, loc=0, scale=1, size=1, random\_state=None)** | Random variates. | | **pdf(x, a, b, loc=0, scale=1)** | Probability density function. | | **logpdf(x, a, b, loc=0, scale=1)** | Log of the probability density function. | | **cdf(x, a, b, loc=0, scale=1)** | Cumulative distribution function. | | **logcdf(x, a, b, loc=0, scale=1)** | Log of the cumulative distribution function. | | **sf(x, a, b, loc=0, scale=1)** | Survival function (also defined as `1 - cdf`, but *sf* is sometimes more accurate). | | **logsf(x, a, b, loc=0, scale=1)** | Log of the survival function. | | **ppf(q, a, b, loc=0, scale=1)** | Percent point function (inverse of `cdf` — percentiles). | | **isf(q, a, b, loc=0, scale=1)** | Inverse survival function (inverse of `sf`). | | **moment(order, a, b, loc=0, scale=1)** | Non-central moment of the specified order. | | **stats(a, b, loc=0, scale=1, moments=’mv’)** | Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’). | | **entropy(a, b, loc=0, scale=1)** | (Differential) entropy of the RV. | | **fit(data)** | Parameter estimates for generic data. See [scipy.stats.rv\_continuous.fit](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_continuous.fit.html#scipy.stats.rv_continuous.fit) for detailed documentation of the keyword arguments. | | **expect(func, args=(a, b), loc=0, scale=1, lb=None, ub=None, conditional=False, \*\*kwds)** | Expected value of a function (of one argument) with respect to the distribution. | | **median(a, b, loc=0, scale=1)** | Median of the distribution. | | **mean(a, b, loc=0, scale=1)** | Mean of the distribution. | | **var(a, b, loc=0, scale=1)** | Variance of the distribution. | | **std(a, b, loc=0, scale=1)** | Standard deviation of the distribution. | | **interval(confidence, a, b, loc=0, scale=1)** | Confidence interval with equal areas around the median. |