statrs/distribution/
cauchy.rs

1use crate::distribution::{Continuous, ContinuousCDF};
2use crate::statistics::*;
3use std::f64;
4
5/// Implements the [Cauchy](https://en.wikipedia.org/wiki/Cauchy_distribution)
6/// distribution, also known as the Lorentz distribution.
7///
8/// # Examples
9///
10/// ```
11/// use statrs::distribution::{Cauchy, Continuous};
12/// use statrs::statistics::Mode;
13///
14/// let n = Cauchy::new(0.0, 1.0).unwrap();
15/// assert_eq!(n.mode().unwrap(), 0.0);
16/// assert_eq!(n.pdf(1.0), 0.1591549430918953357689);
17/// ```
18#[derive(Copy, Clone, PartialEq, Debug)]
19pub struct Cauchy {
20    location: f64,
21    scale: f64,
22}
23
24/// Represents the errors that can occur when creating a [`Cauchy`].
25#[derive(Copy, Clone, PartialEq, Eq, Debug, Hash)]
26#[non_exhaustive]
27pub enum CauchyError {
28    /// The location is NaN.
29    LocationInvalid,
30
31    /// The scale is NaN, zero or less than zero.
32    ScaleInvalid,
33}
34
35impl std::fmt::Display for CauchyError {
36    #[cfg_attr(coverage_nightly, coverage(off))]
37    fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
38        match self {
39            CauchyError::LocationInvalid => write!(f, "Location is NaN"),
40            CauchyError::ScaleInvalid => write!(f, "Scale is NaN, zero or less than zero"),
41        }
42    }
43}
44
45impl std::error::Error for CauchyError {}
46
47impl Cauchy {
48    /// Constructs a new cauchy distribution with the given
49    /// location and scale.
50    ///
51    /// # Errors
52    ///
53    /// Returns an error if location or scale are `NaN` or `scale <= 0.0`
54    ///
55    /// # Examples
56    ///
57    /// ```
58    /// use statrs::distribution::Cauchy;
59    ///
60    /// let mut result = Cauchy::new(0.0, 1.0);
61    /// assert!(result.is_ok());
62    ///
63    /// result = Cauchy::new(0.0, -1.0);
64    /// assert!(result.is_err());
65    /// ```
66    pub fn new(location: f64, scale: f64) -> Result<Cauchy, CauchyError> {
67        if location.is_nan() {
68            return Err(CauchyError::LocationInvalid);
69        }
70
71        if scale.is_nan() || scale <= 0.0 {
72            return Err(CauchyError::ScaleInvalid);
73        }
74
75        Ok(Cauchy { location, scale })
76    }
77
78    /// Returns the location of the cauchy distribution
79    ///
80    /// # Examples
81    ///
82    /// ```
83    /// use statrs::distribution::Cauchy;
84    ///
85    /// let n = Cauchy::new(0.0, 1.0).unwrap();
86    /// assert_eq!(n.location(), 0.0);
87    /// ```
88    pub fn location(&self) -> f64 {
89        self.location
90    }
91
92    /// Returns the scale of the cauchy distribution
93    ///
94    /// # Examples
95    ///
96    /// ```
97    /// use statrs::distribution::Cauchy;
98    ///
99    /// let n = Cauchy::new(0.0, 1.0).unwrap();
100    /// assert_eq!(n.scale(), 1.0);
101    /// ```
102    pub fn scale(&self) -> f64 {
103        self.scale
104    }
105}
106
107impl std::fmt::Display for Cauchy {
108    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
109        write!(f, "Cauchy({}, {})", self.location, self.scale)
110    }
111}
112
113#[cfg(feature = "rand")]
114#[cfg_attr(docsrs, doc(cfg(feature = "rand")))]
115impl ::rand::distributions::Distribution<f64> for Cauchy {
116    fn sample<R: ::rand::Rng + ?Sized>(&self, r: &mut R) -> f64 {
117        self.location + self.scale * (f64::consts::PI * (r.gen::<f64>() - 0.5)).tan()
118    }
119}
120
121impl ContinuousCDF<f64, f64> for Cauchy {
122    /// Calculates the cumulative distribution function for the
123    /// cauchy distribution at `x`
124    ///
125    /// # Formula
126    ///
127    /// ```text
128    /// (1 / π) * arctan((x - x_0) / γ) + 0.5
129    /// ```
130    ///
131    /// where `x_0` is the location and `γ` is the scale
132    fn cdf(&self, x: f64) -> f64 {
133        (1.0 / f64::consts::PI) * ((x - self.location) / self.scale).atan() + 0.5
134    }
135
136    /// Calculates the survival function for the
137    /// cauchy distribution at `x`
138    ///
139    /// # Formula
140    ///
141    /// ```text
142    /// (1 / π) * arctan(-(x - x_0) / γ) + 0.5
143    /// ```
144    ///
145    /// where `x_0` is the location and `γ` is the scale.
146    /// note that this is identical to the cdf except for
147    /// the negative argument to the arctan function
148    fn sf(&self, x: f64) -> f64 {
149        (1.0 / f64::consts::PI) * ((self.location - x) / self.scale).atan() + 0.5
150    }
151
152    /// Calculates the inverse cumulative distribution function for the
153    /// cauchy distribution at `x`
154    ///
155    /// # Formula
156    ///
157    /// ```text
158    /// x_0 + γ tan((x - 0.5) π)
159    /// ```
160    ///
161    /// where `x_0` is the location and `γ` is the scale
162    fn inverse_cdf(&self, x: f64) -> f64 {
163        if !(0.0..=1.0).contains(&x) {
164            panic!("x must be in [0, 1]");
165        } else {
166            self.location + self.scale * (f64::consts::PI * (x - 0.5)).tan()
167        }
168    }
169}
170
171impl Min<f64> for Cauchy {
172    /// Returns the minimum value in the domain of the cauchy
173    /// distribution representable by a double precision float
174    ///
175    /// # Formula
176    ///
177    /// ```text
178    /// NEG_INF
179    /// ```
180    fn min(&self) -> f64 {
181        f64::NEG_INFINITY
182    }
183}
184
185impl Max<f64> for Cauchy {
186    /// Returns the maximum value in the domain of the cauchy
187    /// distribution representable by a double precision float
188    ///
189    /// # Formula
190    ///
191    /// ```text
192    /// f64::INFINITY
193    /// ```
194    fn max(&self) -> f64 {
195        f64::INFINITY
196    }
197}
198
199impl Distribution<f64> for Cauchy {
200    /// Returns the entropy of the cauchy distribution
201    ///
202    /// # Formula
203    ///
204    /// ```text
205    /// ln(γ) + ln(4π)
206    /// ```
207    ///
208    /// where `γ` is the scale
209    fn entropy(&self) -> Option<f64> {
210        Some((4.0 * f64::consts::PI * self.scale).ln())
211    }
212}
213
214impl Median<f64> for Cauchy {
215    /// Returns the median of the cauchy distribution
216    ///
217    /// # Formula
218    ///
219    /// ```text
220    /// x_0
221    /// ```
222    ///
223    /// where `x_0` is the location
224    fn median(&self) -> f64 {
225        self.location
226    }
227}
228
229impl Mode<Option<f64>> for Cauchy {
230    /// Returns the mode of the cauchy distribution
231    ///
232    /// # Formula
233    ///
234    /// ```text
235    /// x_0
236    /// ```
237    ///
238    /// where `x_0` is the location
239    fn mode(&self) -> Option<f64> {
240        Some(self.location)
241    }
242}
243
244impl Continuous<f64, f64> for Cauchy {
245    /// Calculates the probability density function for the cauchy
246    /// distribution at `x`
247    ///
248    /// # Formula
249    ///
250    /// ```text
251    /// 1 / (πγ * (1 + ((x - x_0) / γ)^2))
252    /// ```
253    ///
254    /// where `x_0` is the location and `γ` is the scale
255    fn pdf(&self, x: f64) -> f64 {
256        1.0 / (f64::consts::PI
257            * self.scale
258            * (1.0 + ((x - self.location) / self.scale) * ((x - self.location) / self.scale)))
259    }
260
261    /// Calculates the log probability density function for the cauchy
262    /// distribution at `x`
263    ///
264    /// # Formula
265    ///
266    /// ```text
267    /// ln(1 / (πγ * (1 + ((x - x_0) / γ)^2)))
268    /// ```
269    ///
270    /// where `x_0` is the location and `γ` is the scale
271    fn ln_pdf(&self, x: f64) -> f64 {
272        -(f64::consts::PI
273            * self.scale
274            * (1.0 + ((x - self.location) / self.scale) * ((x - self.location) / self.scale)))
275            .ln()
276    }
277}
278
279#[rustfmt::skip]
280#[cfg(test)]
281mod tests {
282    use super::*;
283    use crate::distribution::internal::*;
284    use crate::testing_boiler;
285
286    testing_boiler!(location: f64, scale: f64; Cauchy; CauchyError);
287
288    #[test]
289    fn test_create() {
290        create_ok(0.0, 0.1);
291        create_ok(0.0, 1.0);
292        create_ok(0.0, 10.0);
293        create_ok(10.0, 11.0);
294        create_ok(-5.0, 100.0);
295        create_ok(0.0, f64::INFINITY);
296    }
297
298    #[test]
299    fn test_bad_create() {
300        let invalid = [
301            (f64::NAN, 1.0, CauchyError::LocationInvalid),
302            (1.0, f64::NAN, CauchyError::ScaleInvalid),
303            (f64::NAN, f64::NAN, CauchyError::LocationInvalid),
304            (1.0, 0.0, CauchyError::ScaleInvalid),
305        ];
306
307        for (location, scale, err) in invalid {
308            test_create_err(location, scale, err);
309        }
310    }
311
312    #[test]
313    fn test_entropy() {
314        let entropy = |x: Cauchy| x.entropy().unwrap();
315        test_exact(0.0, 2.0, 3.224171427529236102395, entropy);
316        test_exact(0.1, 4.0, 3.917318608089181411812, entropy);
317        test_exact(1.0, 10.0, 4.833609339963336476996, entropy);
318        test_exact(10.0, 11.0, 4.92891951976766133704, entropy);
319    }
320
321    #[test]
322    fn test_mode() {
323        let mode = |x: Cauchy| x.mode().unwrap();
324        test_exact(0.0, 2.0, 0.0, mode);
325        test_exact(0.1, 4.0, 0.1, mode);
326        test_exact(1.0, 10.0, 1.0, mode);
327        test_exact(10.0, 11.0, 10.0, mode);
328        test_exact(0.0, f64::INFINITY, 0.0, mode);
329    }
330
331    #[test]
332    fn test_median() {
333        let median = |x: Cauchy| x.median();
334        test_exact(0.0, 2.0, 0.0, median);
335        test_exact(0.1, 4.0, 0.1, median);
336        test_exact(1.0, 10.0, 1.0, median);
337        test_exact(10.0, 11.0, 10.0, median);
338        test_exact(0.0, f64::INFINITY, 0.0, median);
339    }
340
341    #[test]
342    fn test_min_max() {
343        let min = |x: Cauchy| x.min();
344        let max = |x: Cauchy| x.max();
345        test_exact(0.0, 1.0, f64::NEG_INFINITY, min);
346        test_exact(0.0, 1.0, f64::INFINITY, max);
347    }
348
349    #[test]
350    fn test_pdf() {
351        let pdf = |arg: f64| move |x: Cauchy| x.pdf(arg);
352        test_exact(0.0, 0.1, 0.001272730452554141029739, pdf(-5.0));
353        test_exact(0.0, 0.1, 0.03151583031522679916216, pdf(-1.0));
354        test_absolute(0.0, 0.1, 3.183098861837906715378, 1e-14, pdf(0.0));
355        test_exact(0.0, 0.1, 0.03151583031522679916216, pdf(1.0));
356        test_exact(0.0, 0.1, 0.001272730452554141029739, pdf(5.0));
357        test_absolute(0.0, 1.0, 0.01224268793014579505914, 1e-17, pdf(-5.0));
358        test_exact(0.0, 1.0, 0.1591549430918953357689, pdf(-1.0));
359        test_exact(0.0, 1.0, 0.3183098861837906715378, pdf(0.0));
360        test_exact(0.0, 1.0, 0.1591549430918953357689, pdf(1.0));
361        test_absolute(0.0, 1.0, 0.01224268793014579505914, 1e-17, pdf(5.0));
362        test_exact(0.0, 10.0, 0.02546479089470325372302, pdf(-5.0));
363        test_exact(0.0, 10.0, 0.03151583031522679916216, pdf(-1.0));
364        test_exact(0.0, 10.0, 0.03183098861837906715378, pdf(0.0));
365        test_exact(0.0, 10.0, 0.03151583031522679916216, pdf(1.0));
366        test_exact(0.0, 10.0, 0.02546479089470325372302, pdf(5.0));
367        test_exact(-5.0, 100.0, 0.003183098861837906715378, pdf(-5.0));
368        test_absolute(-5.0, 100.0, 0.003178014039374906864395, 1e-17, pdf(-1.0));
369        test_exact(-5.0, 100.0, 0.003175160959439308444267, pdf(0.0));
370        test_exact(-5.0, 100.0, 0.003171680810918599756255, pdf(1.0));
371        test_absolute(-5.0, 100.0, 0.003151583031522679916216, 1e-17, pdf(5.0));
372        test_exact(0.0, f64::INFINITY, 0.0, pdf(-5.0));
373        test_exact(0.0, f64::INFINITY, 0.0, pdf(-1.0));
374        test_exact(0.0, f64::INFINITY, 0.0, pdf(0.0));
375        test_exact(0.0, f64::INFINITY, 0.0, pdf(1.0));
376        test_exact(0.0, f64::INFINITY, 0.0, pdf(5.0));
377        test_exact(f64::INFINITY, 1.0, 0.0, pdf(-5.0));
378        test_exact(f64::INFINITY, 1.0, 0.0, pdf(-1.0));
379        test_exact(f64::INFINITY, 1.0, 0.0, pdf(0.0));
380        test_exact(f64::INFINITY, 1.0, 0.0, pdf(1.0));
381        test_exact(f64::INFINITY, 1.0, 0.0, pdf(5.0));
382    }
383
384    #[test]
385    fn test_ln_pdf() {
386        let ln_pdf = |arg: f64| move |x: Cauchy| x.ln_pdf(arg);
387        test_exact(0.0, 0.1, -6.666590723732973542744, ln_pdf(-5.0));
388        test_absolute(0.0, 0.1, -3.457265309696613941009, 1e-14, ln_pdf(-1.0));
389        test_exact(0.0, 0.1, 1.157855207144645509875, ln_pdf(0.0));
390        test_absolute(0.0, 0.1, -3.457265309696613941009, 1e-14, ln_pdf(1.0));
391        test_exact(0.0, 0.1, -6.666590723732973542744, ln_pdf(5.0));
392        test_exact(0.0, 1.0, -4.402826423870882219615, ln_pdf(-5.0));
393        test_absolute(0.0, 1.0, -1.837877066409345483561, 1e-15, ln_pdf(-1.0));
394        test_exact(0.0, 1.0, -1.144729885849400174143, ln_pdf(0.0));
395        test_absolute(0.0, 1.0, -1.837877066409345483561, 1e-15, ln_pdf(1.0));
396        test_exact(0.0, 1.0, -4.402826423870882219615, ln_pdf(5.0));
397        test_exact(0.0, 10.0, -3.670458530157655613928, ln_pdf(-5.0));
398        test_absolute(0.0, 10.0, -3.457265309696613941009, 1e-14, ln_pdf(-1.0));
399        test_exact(0.0, 10.0, -3.447314978843445858161, ln_pdf(0.0));
400        test_absolute(0.0, 10.0, -3.457265309696613941009, 1e-14, ln_pdf(1.0));
401        test_exact(0.0, 10.0, -3.670458530157655613928, ln_pdf(5.0));
402        test_exact(-5.0, 100.0, -5.749900071837491542179, ln_pdf(-5.0));
403        test_exact(-5.0, 100.0, -5.751498793201188569872, ln_pdf(-1.0));
404        test_exact(-5.0, 100.0, -5.75239695203607874116, ln_pdf(0.0));
405        test_exact(-5.0, 100.0, -5.75349360734762171285, ln_pdf(1.0));
406        test_exact(-5.0, 100.0, -5.759850402690659625027, ln_pdf(5.0));
407        test_exact(0.0, f64::INFINITY, f64::NEG_INFINITY, ln_pdf(-5.0));
408        test_exact(0.0, f64::INFINITY, f64::NEG_INFINITY, ln_pdf(-1.0));
409        test_exact(0.0, f64::INFINITY, f64::NEG_INFINITY, ln_pdf(0.0));
410        test_exact(0.0, f64::INFINITY, f64::NEG_INFINITY, ln_pdf(1.0));
411        test_exact(0.0, f64::INFINITY, f64::NEG_INFINITY, ln_pdf(5.0));
412        test_exact(f64::INFINITY, 1.0, f64::NEG_INFINITY, ln_pdf(-5.0));
413        test_exact(f64::INFINITY, 1.0, f64::NEG_INFINITY, ln_pdf(-1.0));
414        test_exact(f64::INFINITY, 1.0, f64::NEG_INFINITY, ln_pdf(0.0));
415        test_exact(f64::INFINITY, 1.0, f64::NEG_INFINITY, ln_pdf(1.0));
416        test_exact(f64::INFINITY, 1.0, f64::NEG_INFINITY, ln_pdf(5.0));
417    }
418
419    #[test]
420    fn test_cdf() {
421        let cdf = |arg: f64| move |x: Cauchy| x.cdf(arg);
422        test_absolute(0.0, 0.1, 0.006365349100972796679298, 1e-16, cdf(-5.0));
423        test_absolute(0.0, 0.1, 0.03172551743055356951498, 1e-16, cdf(-1.0));
424        test_exact(0.0, 0.1, 0.5, cdf(0.0));
425        test_exact(0.0, 0.1, 0.968274482569446430485, cdf(1.0));
426        test_exact(0.0, 0.1, 0.9936346508990272033207, cdf(5.0));
427        test_absolute(0.0, 1.0, 0.06283295818900118381375, 1e-16, cdf(-5.0));
428        test_exact(0.0, 1.0, 0.25, cdf(-1.0));
429        test_exact(0.0, 1.0, 0.5, cdf(0.0));
430        test_exact(0.0, 1.0, 0.75, cdf(1.0));
431        test_exact(0.0, 1.0, 0.9371670418109988161863, cdf(5.0));
432        test_exact(0.0, 10.0, 0.3524163823495667258246, cdf(-5.0));
433        test_exact(0.0, 10.0, 0.468274482569446430485, cdf(-1.0));
434        test_exact(0.0, 10.0, 0.5, cdf(0.0));
435        test_exact(0.0, 10.0, 0.531725517430553569515, cdf(1.0));
436        test_exact(0.0, 10.0, 0.6475836176504332741754, cdf(5.0));
437        test_exact(-5.0, 100.0, 0.5, cdf(-5.0));
438        test_exact(-5.0, 100.0, 0.5127256113479918307809, cdf(-1.0));
439        test_exact(-5.0, 100.0, 0.5159022512561763751816, cdf(0.0));
440        test_exact(-5.0, 100.0, 0.5190757242358362337495, cdf(1.0));
441        test_exact(-5.0, 100.0, 0.531725517430553569515, cdf(5.0));
442        test_exact(0.0, f64::INFINITY, 0.5, cdf(-5.0));
443        test_exact(0.0, f64::INFINITY, 0.5, cdf(-1.0));
444        test_exact(0.0, f64::INFINITY, 0.5, cdf(0.0));
445        test_exact(0.0, f64::INFINITY, 0.5, cdf(1.0));
446        test_exact(0.0, f64::INFINITY, 0.5, cdf(5.0));
447        test_exact(f64::INFINITY, 1.0, 0.0, cdf(-5.0));
448        test_exact(f64::INFINITY, 1.0, 0.0, cdf(-1.0));
449        test_exact(f64::INFINITY, 1.0, 0.0, cdf(0.0));
450        test_exact(f64::INFINITY, 1.0, 0.0, cdf(1.0));
451        test_exact(f64::INFINITY, 1.0, 0.0, cdf(5.0));
452    }
453
454    #[test]
455    fn test_sf() {
456        let sf = |arg: f64| move |x: Cauchy| x.sf(arg);
457        test_absolute(0.0, 0.1, 0.9936346508990272, 1e-16, sf(-5.0));
458        test_absolute(0.0, 0.1, 0.9682744825694465, 1e-16, sf(-1.0));
459        test_exact(0.0, 0.1, 0.5, sf(0.0));
460        test_absolute(0.0, 0.1, 0.03172551743055352, 1e-16, sf(1.0));
461        test_exact(0.0, 0.1, 0.006365349100972806, sf(5.0));
462        test_absolute(0.0, 1.0, 0.9371670418109989, 1e-16, sf(-5.0));
463        test_exact(0.0, 1.0, 0.75, sf(-1.0));
464        test_exact(0.0, 1.0, 0.5, sf(0.0));
465        test_exact(0.0, 1.0, 0.25, sf(1.0));
466        test_exact(0.0, 1.0, 0.06283295818900114, sf(5.0));
467        test_exact(0.0, 10.0, 0.6475836176504333, sf(-5.0));
468        test_exact(0.0, 10.0, 0.5317255174305535, sf(-1.0));
469        test_exact(0.0, 10.0, 0.5, sf(0.0));
470        test_exact(0.0, 10.0, 0.4682744825694464, sf(1.0));
471        test_exact(0.0, 10.0, 0.35241638234956674, sf(5.0));
472        test_exact(-5.0, 100.0, 0.5, sf(-5.0));
473        test_exact(-5.0, 100.0, 0.4872743886520082, sf(-1.0));
474        test_exact(-5.0, 100.0, 0.4840977487438236, sf(0.0));
475        test_exact(-5.0, 100.0, 0.48092427576416374, sf(1.0));
476        test_exact(-5.0, 100.0, 0.4682744825694464, sf(5.0));
477        test_exact(0.0, f64::INFINITY, 0.5, sf(-5.0));
478        test_exact(0.0, f64::INFINITY, 0.5, sf(-1.0));
479        test_exact(0.0, f64::INFINITY, 0.5, sf(0.0));
480        test_exact(0.0, f64::INFINITY, 0.5, sf(1.0));
481        test_exact(0.0, f64::INFINITY, 0.5, sf(5.0));
482        test_exact(f64::INFINITY, 1.0, 1.0, sf(-5.0));
483        test_exact(f64::INFINITY, 1.0, 1.0, sf(-1.0));
484        test_exact(f64::INFINITY, 1.0, 1.0, sf(0.0));
485        test_exact(f64::INFINITY, 1.0, 1.0, sf(1.0));
486        test_exact(f64::INFINITY, 1.0, 1.0, sf(5.0));
487    }
488
489    #[test]
490    fn test_inverse_cdf() {
491        let func = |arg: f64| move |x: Cauchy| x.inverse_cdf(x.cdf(arg));
492        test_absolute(0.0, 0.1, -5.0, 1e-10, func(-5.0));
493        test_absolute(0.0, 0.1, -1.0, 1e-14, func(-1.0));
494        test_exact(0.0, 0.1, 0.0, func(0.0));
495        test_absolute(0.0, 0.1, 1.0, 1e-14, func(1.0));
496        test_absolute(0.0, 0.1, 5.0, 1e-10, func(5.0));
497        test_absolute(0.0, 1.0, -5.0, 1e-14, func(-5.0));
498        test_absolute(0.0, 1.0, -1.0, 1e-15, func(-1.0));
499        test_exact(0.0, 1.0, 0.0, func(0.0));
500        test_absolute(0.0, 1.0, 1.0, 1e-15, func(1.0));
501        test_absolute(0.0, 1.0, 5.0, 1e-14, func(5.0));
502        test_absolute(0.0, 10.0, -5.0, 1e-14, func(-5.0));
503        test_absolute(0.0, 10.0, -1.0, 1e-14, func(-1.0));
504        test_exact(0.0, 10.0, 0.0, func(0.0));
505        test_absolute(0.0, 10.0, 1.0, 1e-14, func(1.0));
506        test_absolute(0.0, 10.0, 5.0, 1e-14, func(5.0));
507        test_exact(-5.0, 100.0, -5.0, func(-5.0));
508        test_absolute(-5.0, 100.0, -1.0, 1e-10, func(-1.0));
509        test_absolute(-5.0, 100.0, 0.0, 1e-14, func(0.0));
510        test_absolute(-5.0, 100.0, 1.0, 1e-14, func(1.0));
511        test_absolute(-5.0, 100.0, 5.0, 1e-10, func(5.0));
512    }
513
514    #[test]
515    fn test_continuous() {
516        test::check_continuous_distribution(&create_ok(-1.2, 3.4), -1500.0, 1500.0);
517        test::check_continuous_distribution(&create_ok(-4.5, 6.7), -5000.0, 5000.0);
518    }
519}
statrs/distribution/cauchy.rs

statrs/distribution/
cauchy.rs
