# scipy.stats.tukeylambda¶

scipy.stats.tukeylambda

A Tukey-Lambda 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 lam : 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 = tukeylambda(lam, loc=0, scale=1) : Frozen RV object with the same methods but holding the given shape, location, and scale fixed.

Notes

Tukey-Lambda distribution

A flexible distribution ranging from Cauchy (lam=-1) to logistic (lam=0.0) to approx Normal (lam=0.14) to u-shape (lam = 0.5) to Uniform from -1 to 1 (lam = 1)

Examples

```>>> import matplotlib.pyplot as plt
>>> numargs = tukeylambda.numargs
>>> [ lam ] = [0.9,] * numargs
>>> rv = tukeylambda(lam)
```

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

Random number generation

```>>> R = tukeylambda.rvs(lam, size=100)
```

Methods

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

#### Previous topic

scipy.stats.truncnorm

#### Next topic

scipy.stats.uniform