# scipy.stats.mielke¶

scipy.stats.mielke

A Mielke’s Beta-Kappa continuous random variable.

Continuous random variables are defined from a standard form and may require some shape parameters to complete its specification. Any optional keyword parameters can be passed to the methods of the RV object as given below:

Parameters : x : array-like quantiles q : array-like lower or upper tail probability k, s : array-like shape parameters loc : array-like, optional location parameter (default=0) scale : array-like, optional scale parameter (default=1) size : int or tuple of ints, optional shape of random variates (default computed from input arguments ) moments : str, optional composed of letters [‘mvsk’] specifying which moments to compute where ‘m’ = mean, ‘v’ = variance, ‘s’ = (Fisher’s) skew and ‘k’ = (Fisher’s) kurtosis. (default=’mv’) Alternatively, the object may be called (as a function) to fix the shape, : location, and scale parameters returning a “frozen” continuous RV object: : rv = mielke(k, s, loc=0, scale=1) : Frozen RV object with the same methods but holding the given shape, location, and scale fixed.

Notes

Mielke’s Beta-Kappa distribution

mielke.pdf(x,k,s) = k*x**(k-1) / (1+x**s)**(1+k/s) for x > 0.

Examples

```>>> import matplotlib.pyplot as plt
>>> numargs = mielke.numargs
>>> [ k, s ] = [0.9,] * numargs
>>> rv = mielke(k, s)
```

Display frozen pdf

```>>> x = np.linspace(0, np.minimum(rv.dist.b, 3))
>>> h = plt.plot(x, rv.pdf(x))
```

Check accuracy of cdf and ppf

```>>> prb = mielke.cdf(x, k, s)
>>> h = plt.semilogy(np.abs(x - mielke.ppf(prb, k, s)) + 1e-20)
```

Random number generation

```>>> R = mielke.rvs(k, s, size=100)
```

Methods

 rvs(k, s, loc=0, scale=1, size=1) Random variates. pdf(x, k, s, loc=0, scale=1) Probability density function. cdf(x, k, s, loc=0, scale=1) Cumulative density function. sf(x, k, s, loc=0, scale=1) Survival function (1-cdf — sometimes more accurate). ppf(q, k, s, loc=0, scale=1) Percent point function (inverse of cdf — percentiles). isf(q, k, s, loc=0, scale=1) Inverse survival function (inverse of sf). stats(k, s, loc=0, scale=1, moments=’mv’) Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’). entropy(k, s, loc=0, scale=1) (Differential) entropy of the RV. fit(data, k, s, loc=0, scale=1) Parameter estimates for generic data.

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