Boost Math - Statistical Distributions

arcsine_pdf(0.5)
#> [1] 0.6366198
arcsine_lpdf(0.5)
#> [1] -0.4515827
arcsine_cdf(0.5)
#> [1] 0.5
arcsine_lcdf(0.5)
#> [1] -0.6931472
arcsine_quantile(0.5)
#> [1] 0.5

bernoulli_pdf(1, 0.5)
#> [1] 0.5
bernoulli_lpdf(1, 0.5)
#> [1] -0.6931472
bernoulli_cdf(1, 0.5)
#> [1] 1
bernoulli_lcdf(1, 0.5)
#> [1] 0
bernoulli_quantile(0.5, 0.5)
#> [1] 0

# Beta distribution with shape parameters alpha = 2, beta = 5
beta_pdf(0.5, 2, 5)
#> [1] 0.9375
beta_lpdf(0.5, 2, 5)
#> [1] -0.06453852
beta_cdf(0.5, 2, 5)
#> [1] 0.890625
beta_lcdf(0.5, 2, 5)
#> [1] -0.1158318
beta_quantile(0.5, 2, 5)
#> [1] 0.26445

# Binomial dist ribution with n = 10, prob = 0.5
binomial_pdf(3, 10, 0.5)
#> [1] 0.1171875
binomial_lpdf(3, 10, 0.5)
#> [1] -2.14398
binomial_cdf(3, 10, 0.5)
#> [1] 0.171875
binomial_lcdf(3, 10, 0.5)
#> [1] -1.760988
binomial_quantile(0.5, 10, 0.5)
#> [1] 5

# Cauchy distribution with location = 0, scale = 1
cauchy_pdf(0)
#> [1] 0.3183099
cauchy_lpdf(0)
#> [1] -1.14473
cauchy_cdf(0)
#> [1] 0.5
cauchy_lcdf(0)
#> [1] -0.6931472
cauchy_quantile(0.5)
#> [1] 0

# Chi-Squared distribution with 3 degrees of freedom
chi_squared_pdf(2, 3)
#> [1] 0.2075537
chi_squared_lpdf(2, 3)
#> [1] -1.572365
chi_squared_cdf(2, 3)
#> [1] 0.4275933
chi_squared_lcdf(2, 3)
#> [1] -0.8495828
chi_squared_quantile(0.5, 3)
#> [1] 2.365974

# Exponential distribution with rate parameter lambda = 2
exponential_pdf(1, 2)
#> [1] 0.2706706
exponential_lpdf(1, 2)
#> [1] -1.306853
exponential_cdf(1, 2)
#> [1] 0.8646647
exponential_lcdf(1, 2)
#> [1] -0.1454135
exponential_quantile(0.5, 2)
#> [1] 0.3465736

# Extreme Value distribution with location = 0, scale = 1
extreme_value_pdf(0)
#> [1] 0.3678794
extreme_value_lpdf(0)
#> [1] -1
extreme_value_cdf(0)
#> [1] 0.3678794
extreme_value_lcdf(0)
#> [1] -1
extreme_value_quantile(0.5)
#> [1] 0.3665129

# Fisher F distribution with df1 = 5, df2 = 2
fisher_f_pdf(1, 5, 2)
#> [1] 0.3080008
fisher_f_lpdf(1, 5, 2)
#> [1] -1.177653
fisher_f_cdf(1, 5, 2)
#> [1] 0.4312012
fisher_f_lcdf(1, 5, 2)
#> [1] -0.8411806
fisher_f_quantile(0.5, 5, 2)
#> [1] 1.251925

# Gamma distribution with shape = 3, scale = 4
gamma_pdf(2, 3, 4)
#> [1] 0.01895408
gamma_lpdf(2, 3, 4)
#> [1] -3.965736
gamma_cdf(2, 3, 4)
#> [1] 0.01438768
gamma_lcdf(2, 3, 4)
#> [1] -4.241383
gamma_quantile(0.5, 3, 4)
#> [1] 10.69624

# Geometric distribution with probability of success prob = 0.5
geometric_pdf(3, 0.5)
#> [1] 0.0625
geometric_lpdf(3, 0.5)
#> [1] -2.772589
geometric_cdf(3, 0.5)
#> [1] 0.9375
geometric_lcdf(3, 0.5)
#> [1] -0.06453852
geometric_quantile(0.5, 0.5)
#> [1] 0

# Holtsmark distribution with location 0 and scale 1
holtsmark_pdf(3)
#> [1] 0.03150942
holtsmark_lpdf(3)
#> [1] -3.457469
holtsmark_cdf(3)
#> [1] 0.9484022
holtsmark_lcdf(3)
#> [1] -0.05297661
holtsmark_quantile(0.5)
#> [1] 0

# Hyperexponential distribution with probabilities = c(0.5, 0.5) and rates = c(1, 2)
hyperexponential_pdf(2, c(0.5, 0.5), c(1, 2))
#> [1] 0.08598328
hyperexponential_lpdf(2, c(0.5, 0.5), c(1, 2))
#> [1] -2.453602
hyperexponential_cdf(2, c(0.5, 0.5), c(1, 2))
#> [1] 0.9231745
hyperexponential_lcdf(2, c(0.5, 0.5), c(1, 2))
#> [1] -0.07993696
hyperexponential_quantile(0.5, c(0.5, 0.5), c(1, 2))
#> [1] 0.4812118

# Hypergeometric distribution with r = 5, n = 10, N = 20
hypergeometric_pdf(3, 5, 10, 20)
#> [1] 0.3482972
hypergeometric_lpdf(3, 5, 10, 20)
#> [1] -1.054699
hypergeometric_cdf(3, 5, 10, 20)
#> [1] 0.8482972
hypergeometric_lcdf(3, 5, 10, 20)
#> [1] -0.1645242
hypergeometric_quantile(0.5, 5, 10, 20)
#> [1] 3

# Inverse Chi-Squared distribution with 3 degrees of freedom, scale = 1
inverse_chi_squared_pdf(2, 3, 1)
#> [1] 0.1730996
inverse_chi_squared_lpdf(2, 3, 1)
#> [1] -1.753888
inverse_chi_squared_cdf(2, 3, 1)
#> [1] 0.6822703
inverse_chi_squared_lcdf(2, 3, 1)
#> [1] -0.3823293
inverse_chi_squared_quantile(0.5, 3, 1)
#> [1] 1.267977

# Inverse Gamma distribution with shape = 3, scale = 4
inverse_gamma_pdf(2, 3, 4)
#> [1] 0.2706706
inverse_gamma_lpdf(2, 3, 4)
#> [1] -1.306853
inverse_gamma_cdf(2, 3, 4)
#> [1] 0.6766764
inverse_gamma_lcdf(2, 3, 4)
#> [1] -0.3905621
inverse_gamma_quantile(0.5, 3, 4)
#> [1] 1.495853

# Inverse Gaussian distribution with mu = 3, lambda = 4
inverse_gaussian_pdf(2, 3, 4)
#> [1] 0.2524295
inverse_gaussian_lpdf(2, 3, 4)
#> [1] -1.376623
inverse_gaussian_cdf(2, 3, 4)
#> [1] 0.4512408
inverse_gaussian_lcdf(2, 3, 4)
#> [1] -0.7957542
inverse_gaussian_quantile(0.5, 3, 4)
#> [1] 2.202698

# Kolmogorov-Smirnov distribution with sample size n = 10
kolmogorov_smirnov_pdf(0.5, 10)
#> [1] 0.2695176
kolmogorov_smirnov_lpdf(0.5, 10)
#> [1] -1.311122
kolmogorov_smirnov_cdf(0.5, 10)
#> [1] 0.9865241
kolmogorov_smirnov_lcdf(0.5, 10)
#> [1] -0.01356751
kolmogorov_smirnov_quantile(0.5, 10)
#> [1] 0.2617017

# Landau distribution with location 0 and scale 1
landau_pdf(3)
#> [1] 0.05863949
landau_lpdf(3)
#> [1] -2.836347
landau_cdf(3)
#> [1] 0.7792967
landau_lcdf(3)
#> [1] -0.2493635
landau_quantile(0.5)
#> [1] 0.5756301

# Laplace distribution with location = 0, scale = 1
laplace_pdf(0)
#> [1] 0.5
laplace_lpdf(0)
#> [1] -0.6931472
laplace_cdf(0)
#> [1] 0.5
laplace_lcdf(0)
#> [1] -0.6931472
laplace_quantile(0.5)
#> [1] 0

# Logistic distribution with location = 0, scale = 1
logistic_pdf(0)
#> [1] 0.25
logistic_lpdf(0)
#> [1] -1.386294
logistic_cdf(0)
#> [1] 0.5
logistic_lcdf(0)
#> [1] -0.6931472
logistic_quantile(0.5)
#> [1] 0

# Log Normal distribution with location = 0, scale = 1
lognormal_pdf(0)
#> [1] 0
lognormal_lpdf(0)
#> [1] -Inf
lognormal_cdf(0)
#> [1] 0
lognormal_lcdf(0)
#> [1] -Inf
lognormal_quantile(0.5)
#> [1] 1

# Map-Airy distribution with location 0 and scale 1
mapairy_pdf(3)
#> [1] 0.02799732
mapairy_lpdf(3)
#> [1] -3.575647
mapairy_cdf(3)
#> [1] 0.9316961
mapairy_lcdf(3)
#> [1] -0.07074859
mapairy_quantile(0.5)
#> [1] -0.7167107

negative_binomial_pdf(3, 5, 0.5)
#> [1] 0.1367188
negative_binomial_lpdf(3, 5, 0.5)
#> [1] -1.989829
negative_binomial_cdf(3, 5, 0.5)
#> [1] 0.3632812
negative_binomial_lcdf(3, 5, 0.5)
#> [1] -1.012578
negative_binomial_quantile(0.5, 5, 0.5)
#> [1] 4

# Noncentral Beta distribution with shape parameters alpha = 2, beta = 3
# and noncentrality parameter lambda = 1
non_central_beta_pdf(0.5, 2, 3, 1)
#> [1] 1.643543
non_central_beta_lpdf(0.5, 2, 3, 1)
#> [1] 0.4968546
non_central_beta_cdf(0.5, 2, 3, 1)
#> [1] 0.5977904
non_central_beta_lcdf(0.5, 2, 3, 1)
#> [1] -0.514515
non_central_beta_quantile(0.5, 2, 3, 1)
#> [1] 0.4416064

# Noncentral Chi-Squared distribution with 3 degrees of freedom and noncentrality
# parameter 1
non_central_chi_squared_pdf(2, 3, 1)
#> [1] 0.172252
non_central_chi_squared_lpdf(2, 3, 1)
#> [1] -1.758797
non_central_chi_squared_cdf(2, 3, 1)
#> [1] 0.3082525
non_central_chi_squared_lcdf(2, 3, 1)
#> [1] -1.176836
non_central_chi_squared_quantile(0.5, 3, 1)
#> [1] 3.213009

# Noncentral F distribution with df1 = 5, df2 = 2 and noncentrality
# parameter 1
non_central_f_pdf(1, 5, 2, 1)
#> [1] 0.3051418
non_central_f_lpdf(1, 5, 2, 1)
#> [1] -1.186979
non_central_f_cdf(1, 5, 2, 1)
#> [1] 0.3737987
non_central_f_lcdf(1, 5, 2, 1)
#> [1] -0.9840377
non_central_f_quantile(0.5, 5, 2, 1)
#> [1] 1.507635

# Noncentral T distribution with 3 degrees of freedom and noncentrality parameter 1
non_central_t_pdf(0, 3, 1)
#> [1] 0.2229319
non_central_t_lpdf(0, 3, 1)
#> [1] -1.500889
non_central_t_cdf(0, 3, 1)
#> [1] 0.1586553
non_central_t_lcdf(0, 3, 1)
#> [1] -1.841022
non_central_t_quantile(0.5, 3, 1)
#> [1] 1.091153

# Normal distribution with mean = 0, sd = 1
normal_pdf(0)
#> [1] 0.3989423
normal_lpdf(0)
#> [1] -0.9189385
normal_cdf(0)
#> [1] 0.5
normal_lcdf(0)
#> [1] -0.6931472
normal_quantile(0.5)
#> [1] 0

# Pareto distribution with shape = 1, scale = 1
pareto_pdf(1)
#> [1] 1
pareto_lpdf(1)
#> [1] 0
pareto_cdf(1)
#> [1] 0
pareto_lcdf(1)
#> [1] -Inf
pareto_quantile(0.5)
#> [1] 2

# Poisson distribution with lambda = 1
poisson_pdf(0, 1)
#> [1] 0.3678794
poisson_lpdf(0, 1)
#> [1] -1
poisson_cdf(0, 1)
#> [1] 0.3678794
poisson_lcdf(0, 1)
#> [1] -1
poisson_quantile(0.5, 1)
#> [1] 1

# Rayleigh distribution with scale = 1
rayleigh_pdf(1)
#> [1] 0.6065307
rayleigh_lpdf(1)
#> [1] -0.5
rayleigh_cdf(1)
#> [1] 0.3934693
rayleigh_lcdf(1)
#> [1] -0.9327521
rayleigh_quantile(0.5)
#> [1] 1.17741

# SaS Point5 distribution with location 0 and scale 1
saspoint5_pdf(3)
#> [1] 0.02379919
saspoint5_lpdf(3)
#> [1] -3.738104
saspoint5_cdf(3)
#> [1] 0.8164545
saspoint5_lcdf(3)
#> [1] -0.2027841
saspoint5_quantile(0.5)
#> [1] 0

# Skew Normal distribution with location = 0, scale = 1, shape = 0
skew_normal_pdf(0)
#> [1] 0.3989423
skew_normal_lpdf(0)
#> [1] -0.9189385
skew_normal_cdf(0)
#> [1] 0.5
skew_normal_lcdf(0)
#> [1] -0.6931472
skew_normal_quantile(0.5)
#> [1] 0

# Student's t distribution with 3 degrees of freedom
students_t_pdf(0, 3)
#> [1] 0.3675526
students_t_lpdf(0, 3)
#> [1] -1.000889
students_t_cdf(0, 3)
#> [1] 0.5
students_t_lcdf(0, 3)
#> [1] -0.6931472
students_t_quantile(0.5, 3)
#> [1] 0

# Triangular distribution with lower = 0, mode = 1, upper = 2
triangular_pdf(1)
#> [1] 1
triangular_lpdf(1)
#> [1] 0
triangular_cdf(1)
#> [1] 0.5
triangular_lcdf(1)
#> [1] -0.6931472
triangular_quantile(0.5)
#> [1] 1

# Uniform distribution with lower = 0, upper = 1
uniform_pdf(0.5)
#> [1] 1
uniform_lpdf(0.5)
#> [1] 0
uniform_cdf(0.5)
#> [1] 0.5
uniform_lcdf(0.5)
#> [1] -0.6931472
uniform_quantile(0.5)
#> [1] 0.5

# Weibull distribution with shape = 1, scale = 1
weibull_pdf(1)
#> [1] 0.3678794
weibull_lpdf(1)
#> [1] -1
weibull_cdf(1)
#> [1] 0.6321206
weibull_lcdf(1)
#> [1] -0.4586751
weibull_quantile(0.5)
#> [1] 0.6931472