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| BernoulliDist (double p) |
| | Creates a Bernoulli distribution object.
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double | prob (int x) |
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double | cdf (int x) |
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double | barF (int x) |
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int | inverseFInt (double u) |
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double | getMean () |
| | Returns the mean of the distribution function.
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double | getVariance () |
| | Returns the variance of the distribution function.
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double | getStandardDeviation () |
| | Returns the standard deviation of the distribution function.
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double | getP () |
| | Returns the parameter \(p\) of this object.
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double [] | getParams () |
| | Returns an array that contains the parameter \(p\) of the current distribution: [ \(p\)].
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void | setParams (double p) |
| | Resets the parameter to this new value.
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String | toString () |
| | Returns a String containing information about the current distribution.
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| abstract double | prob (int x) |
| | Returns \(p(x)\), the probability of \(x\). More...
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| double | cdf (double x) |
| | Returns the distribution function \(F\) evaluated at \(x\) (see ( FDistDisc )). More...
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| abstract double | cdf (int x) |
| | Returns the distribution function \(F\) evaluated at \(x\) (see ( FDistDisc )). More...
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| double | barF (double x) |
| | Returns \(\bar{F}(x)\), the complementary distribution function. More...
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| double | barF (int x) |
| | Returns \(\bar{F}(x)\), the complementary distribution function. More...
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| int | getXinf () |
| | Returns the lower limit \(x_a\) of the support of the probability mass function. More...
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| int | getXsup () |
| | Returns the upper limit \(x_b\) of the support of the probability mass function. More...
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| double | inverseF (double u) |
| | Returns the inverse distribution function \(F^{-1}(u)\), where. More...
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| int | inverseFInt (double u) |
| | Returns the inverse distribution function \(F^{-1}(u)\), where. More...
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| static double | prob (double p, int x) |
| | Returns the Bernoulli probability \(f(x)\) with parameter \(p\) (see eq. More...
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| static double | cdf (double p, int x) |
| | Returns the Bernoulli distribution function \(F(x)\) with parameter \(p\) (see eq. More...
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static double | barF (double p, int x) |
| | Returns the complementary Bernoulli distribution function \(\bar{F}(x) = P[X \ge x]\) with parameter \(p\).
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static int | inverseF (double p, double u) |
| | Returns the inverse of the Bernoulli distribution function with parameter \(p\) at \(u\).
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| static double [] | getMLE (int[] x, int m) |
| | Estimates the parameters \(p\) of the Bernoulli distribution using the maximum likelihood method, from the \(m\) observations \(x[i]\), \(i = 0, 1,…, m-1\). More...
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| static BernoulliDist | getInstanceFromMLE (int[] x, int m) |
| | Creates a new instance of a Bernoulli distribution with parameter \(p\) estimated using the maximum likelihood method, from the \(m\) observations \(x[i]\), \(i = 0, 1, …, m-1\). More...
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| static double | getMean (double p) |
| | Returns the mean \(E[X] = p\) of the Bernoulli distribution with parameter \(p\). More...
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| static double | getVariance (double p) |
| | Computes the variance \(\mbox{Var}[X] = p(1 - p)\) of the Bernoulli distribution with parameter \(p\). More...
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| static double | getStandardDeviation (double p) |
| | Computes the standard deviation of the Bernoulli distribution with parameter \(p\). More...
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Extends the class DiscreteDistributionInt for the Bernoulli distribution [118] with parameter \(p\), where \(0\le p\le1\).
Its mass function is given by
\[ f(x) = \begin{cases} 1 - p, \qquad & \text{if $x = 0$;} \\ p, & \text{if $x = 1$;} \tag{fmass-bernoulli} \\ 0, & \text{otherwise.} \end{cases} \]
Its distribution function is
\[ F(x) = \begin{cases} 0, & \text{if $x < 0$;} \\ 1 - p, \qquad & \text{if $0 \le x < 1$;} \tag{cdf-bernoulli} \\ 1, & \text{if $x \ge1$.} \end{cases} \]
| static double [] getMLE |
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int [] |
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Estimates the parameters \(p\) of the Bernoulli distribution using the maximum likelihood method, from the \(m\) observations \(x[i]\), \(i = 0, 1,…, m-1\).
The estimate is returned in a one-element array: [ \(p\)].
- Parameters
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| x | the list of observations used to evaluate parameters |
| m | the number of observations used to evaluate parameters |
- Returns
- returns the parameter [ \(\hat{p}\)]
Public Member Functions inherited from DiscreteDistributionInt