```  1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
```
```use distribution::{Binomial, Discrete, Univariate};
use rand::distributions::Distribution;
use rand::Rng;
use statistics::*;
use Result;

/// Implements the
/// [Bernoulli](https://en.wikipedia.org/wiki/Bernoulli_distribution)
/// distribution which is a special case of the
/// [Binomial](https://en.wikipedia.org/wiki/Binomial_distribution)
/// distribution where `n = 1` (referenced [Here](./struct.Binomial.html))
///
/// # Examples
///
/// ```
/// use statrs::distribution::{Bernoulli, Discrete};
/// use statrs::statistics::Mean;
///
/// let n = Bernoulli::new(0.5).unwrap();
/// assert_eq!(n.mean(), 0.5);
/// assert_eq!(n.pmf(0), 0.5);
/// assert_eq!(n.pmf(1), 0.5);
/// ```
#[derive(Debug, Copy, Clone, PartialEq)]
pub struct Bernoulli {
b: Binomial,
}

impl Bernoulli {
/// Constructs a new bernoulli distribution with
/// the given `p` probability of success.
///
/// # Errors
///
/// Returns an error if `p` is `NaN`, less than `0.0`
/// or greater than `1.0`
///
/// # Examples
///
/// ```
/// use statrs::distribution::Bernoulli;
///
/// let mut result = Bernoulli::new(0.5);
/// assert!(result.is_ok());
///
/// result = Bernoulli::new(-0.5);
/// assert!(result.is_err());
/// ```
pub fn new(p: f64) -> Result<Bernoulli> {
Binomial::new(p, 1).map(|b| Bernoulli { b: b })
}

/// Returns the probability of success `p` of the
/// bernoulli distribution.
///
/// # Examples
///
/// ```
/// use statrs::distribution::Bernoulli;
///
/// let n = Bernoulli::new(0.5).unwrap();
/// assert_eq!(n.p(), 0.5);
/// ```
pub fn p(&self) -> f64 {
self.b.p()
}

/// Returns the number of trials `n` of the
/// bernoulli distribution. Will always be `1.0`.
///
/// # Examples
///
/// ```
/// use statrs::distribution::Bernoulli;
///
/// let n = Bernoulli::new(0.5).unwrap();
/// assert_eq!(n.n(), 1);
/// ```
pub fn n(&self) -> u64 {
1
}
}

impl Distribution<f64> for Bernoulli {
fn sample<R: Rng + ?Sized>(&self, r: &mut R) -> f64 {
r.gen_bool(self.p()) as u8 as f64
}
}

impl Univariate<u64, f64> for Bernoulli {
/// Calculates the cumulative distribution
/// function for the bernoulli distribution at `x`.
///
/// # Formula
///
/// ```ignore
/// if x < 0 { 0 }
/// else if x >= 1 { 1 }
/// else { 1 - p }
/// ```
fn cdf(&self, x: f64) -> f64 {
self.b.cdf(x)
}
}

impl Min<u64> for Bernoulli {
/// Returns the minimum value in the domain of the
/// bernoulli distribution representable by a 64-
/// bit integer
///
/// # Formula
///
/// ```ignore
/// 0
/// ```
fn min(&self) -> u64 {
0
}
}

impl Max<u64> for Bernoulli {
/// Returns the maximum value in the domain of the
/// bernoulli distribution representable by a 64-
/// bit integer
///
/// # Formula
///
/// ```ignore
/// 1
/// ```
fn max(&self) -> u64 {
1
}
}

impl Mean<f64> for Bernoulli {
/// Returns the mean of the bernoulli
/// distribution
///
/// # Formula
///
/// ```ignore
/// p
/// ```
fn mean(&self) -> f64 {
self.b.mean()
}
}

impl Variance<f64> for Bernoulli {
/// Returns the variance of the bernoulli
/// distribution
///
/// # Formula
///
/// ```ignore
/// p * (1 - p)
/// ```
fn variance(&self) -> f64 {
self.b.variance()
}

/// Returns the standard deviation of the bernoulli
/// distribution
///
/// # Formula
///
/// ```ignore
/// sqrt(p * (1 - p))
/// ```
fn std_dev(&self) -> f64 {
self.b.std_dev()
}
}

impl Entropy<f64> for Bernoulli {
/// Returns the entropy of the bernoulli
/// distribution
///
/// # Formula
///
/// ```ignore
/// q = (1 - p)
/// -q * ln(q) - p * ln(p)
/// ```
fn entropy(&self) -> f64 {
self.b.entropy()
}
}

impl Skewness<f64> for Bernoulli {
/// Returns the skewness of the bernoulli
/// distribution
///
/// # Formula
///
/// ```ignore
/// q = (1 - p)
/// (1 - 2p) / sqrt(p * q)
/// ```
fn skewness(&self) -> f64 {
self.b.skewness()
}
}

impl Median<f64> for Bernoulli {
/// Returns the median of the bernoulli
/// distribution
///
/// # Formula
///
/// ```ignore
/// if p < 0.5 { 0 }
/// else if p > 0.5 { 1 }
/// else { 0.5 }
/// ```
fn median(&self) -> f64 {
self.b.median()
}
}

impl Mode<u64> for Bernoulli {
/// Returns the mode of the bernoulli distribution
///
/// # Formula
///
/// ```ignore
/// if p < 0.5 { 0 }
/// else { 1 }
/// ```
fn mode(&self) -> u64 {
self.b.mode()
}
}

impl Discrete<u64, f64> for Bernoulli {
/// Calculates the probability mass function for the
/// bernoulli distribution at `x`.
///
/// # Formula
///
/// ```ignore
/// if x == 0 { 1 - p }
/// else { p }
/// ```
fn pmf(&self, x: u64) -> f64 {
self.b.pmf(x)
}

/// Calculates the log probability mass function for the
/// bernoulli distribution at `x`.
///
/// # Formula
///
/// ```ignore
/// else if x == 0 { ln(1 - p) }
/// else { ln(p) }
/// ```
fn ln_pmf(&self, x: u64) -> f64 {
self.b.ln_pmf(x)
}
}
```