Module: Distribution::Beta::Ruby_
- Extended by:
- Math
- Defined in:
- lib/distribution/beta/ruby.rb
Constant Summary
Constants included from MathExtension
MathExtension::EULER, MathExtension::LN2, MathExtension::LNPI, MathExtension::LOG_FLOAT_MIN, MathExtension::ROOT3_FLOAT_EPSILON, MathExtension::ROOT3_FLOAT_MIN, MathExtension::ROOT4_FLOAT_EPSILON, MathExtension::ROOT4_FLOAT_MIN, MathExtension::ROOT5_FLOAT_EPSILON, MathExtension::ROOT5_FLOAT_MIN, MathExtension::ROOT6_FLOAT_EPSILON, MathExtension::ROOT6_FLOAT_MIN, MathExtension::SQRT2, MathExtension::SQRTPI
Class Method Summary collapse
-
.cdf(x, a, b) ⇒ Object
Gamma cumulative distribution function Translated from GSL-1.9: cdf/beta.c gsl_cdf_beta_P.
-
.p_value(p, a, b, rmin = 0, rmax = 1) ⇒ Object
Inverse of the beta distribution function.
-
.pdf(x, a, b) ⇒ Object
Beta distribution probability density function.
Methods included from Math
beta, binomial_coefficient, binomial_coefficient_gamma, combinations, erfc_e, exact_regularized_beta, factorial, fast_factorial, gammp, gammq, incomplete_beta, incomplete_gamma, lbeta, logbeta, loggamma, permutations, regularized_beta, rising_factorial, unnormalized_incomplete_gamma
Methods included from MathExtension
#beta, #binomial_coefficient, #binomial_coefficient_gamma, #binomial_coefficient_multiplicative, #erfc_e, #exact_regularized_beta, #exp_err, #factorial, #fast_factorial, #gammq, #incomplete_beta, #incomplete_gamma, #lbeta, #logbeta, #loggamma, #permutations, #regularized_beta, #rising_factorial, #unnormalized_incomplete_gamma
Class Method Details
.cdf(x, a, b) ⇒ Object
Gamma cumulative distribution function Translated from GSL-1.9: cdf/beta.c gsl_cdf_beta_P
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# File 'lib/distribution/beta/ruby.rb', line 31 def cdf(x, a, b) return 0.0 if x <= 0.0 return 1.0 if x >= 1.0 Math::IncompleteBeta.axpy(1.0, 0.0, a, b, x) end |
.p_value(p, a, b, rmin = 0, rmax = 1) ⇒ Object
Inverse of the beta distribution function
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# File 'lib/distribution/beta/ruby.rb', line 38 def p_value(p, a, b, rmin = 0, rmax = 1) fail 'a <= 0' if a <= 0 fail 'b <= 0' if b <= 0 fail 'rmin == rmax' if rmin == rmax fail 'p <= 0' if p <= 0 fail 'p > 1' if p > 1 precision = 8.88e-016 max_iterations = 256 ga = 0 gb = 2 i = 1 while ((gb - ga) > precision) && (i < max_iterations) guess = (ga + gb) / 2.0 result = cdf(guess, a, b) if (result == p) || (result == 0) gb = ga elsif result > p gb = guess else ga = guess end fail 'No value' if i == max_iterations i += 1 end rmin + guess * (rmax - rmin) end |
.pdf(x, a, b) ⇒ Object
Beta distribution probability density function
Adapted from GSL-1.9 (apparently by Knuth originally), found in randist/beta.c
Form: p(x) dx = (Gamma(a + b)/(Gamma(a) Gamma(b))) x^(a-1) (1-x)^(b-1) dx
References
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# File 'lib/distribution/beta/ruby.rb', line 15 def pdf(x, a, b) return 0 if x < 0 || x > 1 gab = Math.lgamma(a + b).first ga = Math.lgamma(a).first gb = Math.lgamma(b).first if x == 0.0 || x == 1.0 Math.exp(gab - ga - gb) * x**(a - 1) * (1 - x)**(b - 1) else Math.exp(gab - ga - gb + Math.log(x) * (a - 1) + Math::Log.log1p(-x) * (b - 1)) end end |