# scipy.stats.genexpon¶

scipy.stats.genexpon

A generalized exponential 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 a, b, c : 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 = genexpon(a, b, c, loc=0, scale=1) : Frozen RV object with the same methods but holding the given shape, location, and scale fixed.

Notes

Generalized exponential distribution (Ryu 1993)

f(x,a,b,c) = (a+b*(1-exp(-c*x))) * exp(-a*x-b*x+b/c*(1-exp(-c*x))) for x >= 0, a,b,c > 0.

a, b, c are the first, second and third shape parameters.

References

“The Exponential Distribution: Theory, Methods and Applications”, N. Balakrishnan, Asit P. Basu

Examples

```>>> import matplotlib.pyplot as plt
>>> numargs = genexpon.numargs
>>> [ a, b, c ] = [0.9,] * numargs
>>> rv = genexpon(a, b, c)
```

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 = genexpon.cdf(x, a, b, c)
>>> h = plt.semilogy(np.abs(x - genexpon.ppf(prb, a, b, c)) + 1e-20)
```

Random number generation

```>>> R = genexpon.rvs(a, b, c, size=100)
```

Methods

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

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