Package index

All functions

airy_ai() airy_bi() airy_ai_prime() airy_bi_prime() airy_ai_zero() airy_bi_zero()

Airy Functions

anderson_darling_normality_statistic()

Anderson-Darling Test for Normality

arcsine_distribution() arcsine_pdf() arcsine_lpdf() arcsine_cdf() arcsine_lcdf() arcsine_quantile()

Arcsine Distribution Functions

barycentric_rational()

Barycentric Rational Interpolation

sin_pi() cos_pi() log1p_boost() expm1_boost() cbrt() sqrt1pm1() powm1() hypot() rsqrt()

Basic Mathematical Functions

bernoulli_distribution() bernoulli_pdf() bernoulli_lpdf() bernoulli_cdf() bernoulli_lcdf() bernoulli_quantile()

Bernoulli Distribution Functions

cyl_bessel_j() cyl_neumann() cyl_bessel_j_zero() cyl_neumann_zero() cyl_bessel_i() cyl_bessel_k() sph_bessel() sph_neumann() cyl_bessel_j_prime() cyl_neumann_prime() cyl_bessel_i_prime() cyl_bessel_k_prime() sph_bessel_prime() sph_neumann_prime()

Bessel Functions, Their Derivatives, and Zeros

beta_distribution() beta_pdf() beta_lpdf() beta_cdf() beta_lcdf() beta_quantile() beta_find_alpha() beta_find_beta()

Beta Distribution Functions

beta_boost() ibeta() ibetac() betac() ibeta_inv() ibetac_inv() ibeta_inva() ibetac_inva() ibeta_invb() ibetac_invb() ibeta_derivative()

Beta Functions

bezier_polynomial()

Bezier Polynomial Interpolator

bilinear_uniform()

Bilinear Uniform Interpolator

binomial_distribution() binomial_pdf() binomial_lpdf() binomial_cdf() binomial_lcdf() binomial_quantile() binomial_find_lower_bound_on_p() binomial_find_upper_bound_on_p() binomial_find_minimum_number_of_trials() binomial_find_maximum_number_of_trials()

Binomial Distribution Functions

covariance() means_and_covariance() correlation_coefficient()

Bivariate Statistics Functions

cardinal_cubic_b_spline()

Cardinal Cubic B-Spline Interpolator

cardinal_cubic_hermite()

Cardinal Cubic Hermite Interpolator

cardinal_quadratic_b_spline()

Cardinal Quadratic B-Spline Interpolator

cardinal_quintic_b_spline()

Cardinal Quintic B-Spline Interpolator

cardinal_quintic_hermite()

Cardinal Quintic Hermite Interpolator

catmull_rom()

Catmull-Rom Interpolation

cauchy_distribution() cauchy_pdf() cauchy_lpdf() cauchy_cdf() cauchy_lcdf() cauchy_quantile()

Cauchy Distribution Functions

chatterjee_correlation()

Chatterjee Correlation Function

chebyshev_next() chebyshev_t() chebyshev_u() chebyshev_t_prime() chebyshev_clenshaw_recurrence() chebyshev_clenshaw_recurrence_ab()

Chebyshev Polynomials and Related Functions

chi_squared_distribution() chi_squared_pdf() chi_squared_lpdf() chi_squared_cdf() chi_squared_lcdf() chi_squared_quantile() chi_squared_find_degrees_of_freedom()

Chi-Squared Distribution Functions

constants()

Boost Math Constants

cubic_hermite()

Cubic Hermite Interpolator

tanh_sinh() sinh_sinh() exp_sinh()

Double Exponential Quadrature

ellint_rf() ellint_rd() ellint_rj() ellint_rc() ellint_rg() ellint_1() ellint_2() ellint_3() ellint_d() jacobi_zeta() heuman_lambda()

Elliptic Integrals

erf() erfc() erf_inv() erfc_inv()

Error Functions and Inverses

exponential_distribution() exponential_pdf() exponential_lpdf() exponential_cdf() exponential_lcdf() exponential_quantile()

Exponential Distribution Functions

expint_en() expint_ei()

Exponential Integrals

extreme_value_distribution() extreme_value_pdf() extreme_value_lpdf() extreme_value_cdf() extreme_value_lcdf() extreme_value_quantile()

Extreme Value Distribution Functions

factorial_boost() unchecked_factorial() max_factorial() double_factorial() rising_factorial() falling_factorial() binomial_coefficient()

Factorials and Binomial Coefficients

daubechies_scaling_filter() daubechies_wavelet_filter()

Filters

fisher_f_distribution() fisher_f_pdf() fisher_f_lpdf() fisher_f_cdf() fisher_f_lcdf() fisher_f_quantile()

Fisher F Distribution Functions

gamma_distribution() gamma_pdf() gamma_lpdf() gamma_cdf() gamma_lcdf() gamma_quantile()

Gamma Distribution Functions

tgamma() tgamma1pm1() lgamma_boost() digamma_boost() trigamma_boost() polygamma() tgamma_ratio() tgamma_delta_ratio() gamma_p() gamma_q() tgamma_lower() tgamma_upper() gamma_q_inv() gamma_p_inv() gamma_q_inva() gamma_p_inva() gamma_p_derivative()

Gamma Functions

gegenbauer() gegenbauer_prime() gegenbauer_derivative()

Gegenbauer Polynomials and Related Functions

cdf() logcdf() pdf() logpdf() hazard() chf() mode() standard_deviation() support() variance() skewness() kurtosis() kurtosis_excess()

Generic Distribution Functions

geometric_distribution() geometric_pdf() geometric_lpdf() geometric_cdf() geometric_lcdf() geometric_quantile() geometric_find_lower_bound_on_p() geometric_find_upper_bound_on_p() geometric_find_minimum_number_of_trials() geometric_find_maximum_number_of_trials()

Geometric Distribution Functions

cyl_hankel_1() cyl_hankel_2() sph_hankel_1() sph_hankel_2()

Hankel Functions

hermite() hermite_next()

Hermite Polynomials and Related Functions

holtsmark_distribution() holtsmark_pdf() holtsmark_lpdf() holtsmark_cdf() holtsmark_lcdf() holtsmark_quantile()

Holtsmark Distribution Functions

hyperexponential_distribution() hyperexponential_pdf() hyperexponential_lpdf() hyperexponential_cdf() hyperexponential_lcdf() hyperexponential_quantile()

Hyperexponential Distribution Functions

hypergeometric_distribution() hypergeometric_pdf() hypergeometric_lpdf() hypergeometric_cdf() hypergeometric_lcdf() hypergeometric_quantile()

Hypergeometric Distribution Functions

hypergeometric_1F0() hypergeometric_0F1() hypergeometric_2F0() hypergeometric_1F1() hypergeometric_1F1_regularized() log_hypergeometric_1F1() hypergeometric_pFq()

Hypergeometric Functions

inverse_chi_squared_distribution() inverse_chi_squared_pdf() inverse_chi_squared_lpdf() inverse_chi_squared_cdf() inverse_chi_squared_lcdf() inverse_chi_squared_quantile()

Inverse Chi-Squared Distribution Functions

inverse_gamma_distribution() inverse_gamma_pdf() inverse_gamma_lpdf() inverse_gamma_cdf() inverse_gamma_lcdf() inverse_gamma_quantile()

Inverse Gamma Distribution Functions

inverse_gaussian_distribution() inverse_gaussian_pdf() inverse_gaussian_lpdf() inverse_gaussian_cdf() inverse_gaussian_lcdf() inverse_gaussian_quantile()

Inverse Gaussian Distribution Functions

acosh_boost() asinh_boost() atanh_boost()

Inverse Hyperbolic Functions

jacobi_elliptic() jacobi_cd() jacobi_cn() jacobi_cs() jacobi_dc() jacobi_dn() jacobi_ds() jacobi_nc() jacobi_nd() jacobi_ns() jacobi_sc() jacobi_sd() jacobi_sn()

Jacobi Elliptic Functions

jacobi() jacobi_prime() jacobi_double_prime() jacobi_derivative()

Jacobi Polynomials and Related Functions

jacobi_theta1() jacobi_theta1tau() jacobi_theta2() jacobi_theta2tau() jacobi_theta3() jacobi_theta3tau() jacobi_theta3m1() jacobi_theta3m1tau() jacobi_theta4() jacobi_theta4tau() jacobi_theta4m1() jacobi_theta4m1tau()

Jacobi Theta Functions

kolmogorov_smirnov_distribution() kolmogorov_smirnov_pdf() kolmogorov_smirnov_lpdf() kolmogorov_smirnov_cdf() kolmogorov_smirnov_lcdf() kolmogorov_smirnov_quantile()

Kolmogorov-Smirnov Distribution Functions

laguerre() laguerre_m() laguerre_next() laguerre_next_m()

Laguerre Polynomials and Related Functions

lambert_w0() lambert_wm1() lambert_w0_prime() lambert_wm1_prime()

Lambert W Function and Its Derivatives

landau_distribution() landau_pdf() landau_lpdf() landau_cdf() landau_lcdf() landau_quantile()

Landau Distribution Functions

laplace_distribution() laplace_pdf() laplace_lpdf() laplace_cdf() laplace_lcdf() laplace_quantile()

Laplace Distribution Functions

legendre_p() legendre_p_prime() legendre_p_zeros() legendre_p_m() legendre_q() legendre_next() legendre_next_m()

Legendre Polynomials and Related Functions

simple_ordinary_least_squares() simple_ordinary_least_squares_with_R_squared()

Linear Regression Functions

ljung_box()

Ljung-Box Test for Autocorrelation

logistic_distribution() logistic_pdf() logistic_lpdf() logistic_cdf() logistic_lcdf() logistic_quantile()

Logistic Distribution Functions

lognormal_distribution() lognormal_pdf() lognormal_lpdf() lognormal_cdf() lognormal_lcdf() lognormal_quantile()

Log Normal Distribution Functions

makima()

Modified Akima Interpolator

mapairy_distribution() mapairy_pdf() mapairy_lpdf() mapairy_cdf() mapairy_lcdf() mapairy_quantile()

Map-Airy Distribution Functions

negative_binomial_distribution() negative_binomial_pdf() negative_binomial_lpdf() negative_binomial_cdf() negative_binomial_lcdf() negative_binomial_quantile() negative_binomial_find_lower_bound_on_p() negative_binomial_find_upper_bound_on_p() negative_binomial_find_minimum_number_of_trials() negative_binomial_find_maximum_number_of_trials()

Negative Binomial Distribution Functions

non_central_beta_distribution() non_central_beta_pdf() non_central_beta_lpdf() non_central_beta_cdf() non_central_beta_lcdf() non_central_beta_quantile()

Noncentral Beta Distribution Functions

non_central_chi_squared_distribution() non_central_chi_squared_pdf() non_central_chi_squared_lpdf() non_central_chi_squared_cdf() non_central_chi_squared_lcdf() non_central_chi_squared_quantile() non_central_chi_squared_find_degrees_of_freedom() non_central_chi_squared_find_non_centrality()

Noncentral Chi-Squared Distribution Functions

non_central_f_distribution() non_central_f_pdf() non_central_f_lpdf() non_central_f_cdf() non_central_f_lcdf() non_central_f_quantile()

Noncentral F Distribution Functions

non_central_t_distribution() non_central_t_pdf() non_central_t_lpdf() non_central_t_cdf() non_central_t_lcdf() non_central_t_quantile()

Noncentral T Distribution Functions

normal_distribution() normal_pdf() normal_lpdf() normal_cdf() normal_lcdf() normal_quantile()

Normal Distribution Functions

bernoulli_b2n() max_bernoulli_b2n() unchecked_bernoulli_b2n() tangent_t2n() prime() max_prime() fibonacci() unchecked_fibonacci()

Number Series

finite_difference_derivative() complex_step_derivative()

Numerical Differentiation

trapezoidal() gauss_legendre() gauss_kronrod()

Numerical Integration

ooura_fourier_sin() ooura_fourier_cos()

Ooura Fourier Integrals

owens_t()

Owens T Function

pareto_distribution() pareto_pdf() pareto_lpdf() pareto_cdf() pareto_lcdf() pareto_quantile()

Pareto Distribution Functions

pchip()

PCHIP Interpolator

poisson_distribution() poisson_pdf() poisson_lpdf() poisson_cdf() poisson_lcdf() poisson_quantile()

Poisson Distribution Functions

quadratic_roots() cubic_roots() cubic_root_residual() cubic_root_condition_number() quartic_roots()

Polynomial Root-Finding

quintic_hermite()

Quintic Hermite Interpolator

rayleigh_distribution() rayleigh_pdf() rayleigh_lpdf() rayleigh_cdf() rayleigh_lcdf() rayleigh_quantile()

Rayleigh Distribution Functions

bisect() bracket_and_solve_root() toms748_solve() newton_raphson_iterate() halley_iterate() schroder_iterate() brent_find_minima()

Root-Finding and Minimisation Functions

runs_above_and_below_threshold() runs_above_and_below_median()

Runs Tests

saspoint5_distribution() saspoint5_pdf() saspoint5_lpdf() saspoint5_cdf() saspoint5_lcdf() saspoint5_quantile()

S\(\alpha\)S Point5 Distribution Functions

absolute_gini_coefficient() sample_absolute_gini_coefficient() hoyer_sparsity() oracle_snr() oracle_snr_db() m2m4_snr_estimator() m2m4_snr_estimator_db()

Signal Statistics Functions

sinc_pi() sinhc_pi()

Sinus Cardinal and Hyperbolic Functions

skew_normal_distribution() skew_normal_pdf() skew_normal_lpdf() skew_normal_cdf() skew_normal_lcdf() skew_normal_quantile()

Skew Normal Distribution Functions

spherical_harmonic() spherical_harmonic_r() spherical_harmonic_i()

Spherical Harmonics

students_t_distribution() students_t_pdf() students_t_lpdf() students_t_cdf() students_t_lcdf() students_t_quantile() students_t_find_degrees_of_freedom()

Student's T Distribution Functions

one_sample_t_test_params() one_sample_t_test() two_sample_t_test() paired_samples_t_test()

T-Tests

triangular_distribution() triangular_pdf() triangular_lpdf() triangular_cdf() triangular_lcdf() triangular_quantile()

Triangular Distribution Functions

uniform_distribution() uniform_pdf() uniform_lpdf() uniform_cdf() uniform_lcdf() uniform_quantile()

Uniform Distribution Functions

mean_boost() variance(<default>) sample_variance() mean_and_sample_variance() skewness(<default>) kurtosis(<default>) excess_kurtosis() first_four_moments() median_boost() median_absolute_deviation() interquartile_range() gini_coefficient() sample_gini_coefficient() mode(<default>)

Univariate Statistics Functions

l0_pseudo_norm() hamming_distance() l1_norm() l1_distance() l2_norm() l2_distance() sup_norm() sup_distance() lp_norm() lp_distance() total_variation()

Vector Functionals

weibull_distribution() weibull_pdf() weibull_lpdf() weibull_cdf() weibull_lcdf() weibull_quantile()

Weibull Distribution Functions

one_sample_z_test_params() one_sample_z_test() two_sample_z_test()

Z-Tests

zeta()

Riemann Zeta Function