# 11.6.10. astroML.stats.linear¶

`astroML.stats.``linear`(*args, **kwds)

A truncated positive exponential continuous random variable.

The probability distribution is:

```p(x) ~ c * x + d   between a and b
= 0             otherwise
```

The arguments are (a, b, c). d is set by the normalization

As an instance of the rv_continuous class, linear 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.

Examples

```>>> from scipy.stats import linear
>>> import matplotlib.pyplot as plt
>>> fig, ax = plt.subplots(1, 1)
```

Calculate a few first moments:

```>>> a, b, c =
>>> mean, var, skew, kurt = linear.stats(a, b, c, moments='mvsk')
```

Display the probability density function (`pdf`):

```>>> x = np.linspace(linear.ppf(0.01, a, b, c),
...                 linear.ppf(0.99, a, b, c), 100)
>>> ax.plot(x, linear.pdf(x, a, b, c),
...        'r-', lw=5, alpha=0.6, label='linear 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 = linear(a, b, c)
>>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
```

Check accuracy of `cdf` and `ppf`:

```>>> vals = linear.ppf([0.001, 0.5, 0.999], a, b, c)
>>> np.allclose([0.001, 0.5, 0.999], linear.cdf(vals, a, b, c))
True
```

Generate random numbers:

```>>> r = linear.rvs(a, b, c, size=1000)
```

And compare the histogram:

```>>> ax.hist(r, density=True, histtype='stepfilled', alpha=0.2)
>>> ax.legend(loc='best', frameon=False)
>>> plt.show()
```

Methods

 rvs(a, b, c, loc=0, scale=1, size=1, random_state=None) Random variates. pdf(x, a, b, c, loc=0, scale=1) Probability density function. logpdf(x, a, b, c, loc=0, scale=1) Log of the probability density function. cdf(x, a, b, c, loc=0, scale=1) Cumulative distribution function. logcdf(x, a, b, c, loc=0, scale=1) Log of the cumulative distribution function. sf(x, a, b, c, loc=0, scale=1) Survival function (also defined as `1 - cdf`, but sf is sometimes more accurate). logsf(x, a, b, c, loc=0, scale=1) Log of the survival function. 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`). moment(n, a, b, c, loc=0, scale=1) Non-central moment of order n 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) Parameter estimates for generic data. See scipy.stats.rv_continuous.fit for detailed documentation of the keyword arguments. expect(func, args=(a, b, c), 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, c, loc=0, scale=1) Median of the distribution. mean(a, b, c, loc=0, scale=1) Mean of the distribution. var(a, b, c, loc=0, scale=1) Variance of the distribution. std(a, b, c, loc=0, scale=1) Standard deviation of the distribution. interval(alpha, a, b, c, loc=0, scale=1) Endpoints of the range that contains alpha percent of the distribution