Closed form distributions, based on the incomplete beta function

• Boost: Beta (Pearson Type I and II) distribution
  • Ctx.beta_pdf()
  • Ctx.beta_cdf()
  • Ctx.beta_qtf()
  • ctx.dist_beta
  • dist_beta.pdf()
  • dist_beta.cdf()
  • dist_beta.sf()
  • dist_beta.qtf()
  • dist_beta.isf()
  • dist_beta.c_x()
  • dist_beta.m_x()
  • dist_beta.k_x()
  • dist_beta.moments()
  • dist_beta.cumulants()
  • ctx.beta_recurrence()
• Boost: Central Fisher F distribution
  • Ctx.fisher_f_pdf()
  • Ctx.fisher_f_cdf()
  • Ctx.fisher_f_qtf()
  • ctx.dist_fisher_f
  • dist_fisher_f.pdf()
  • dist_fisher_f.cdf()
  • dist_fisher_f.sf()
  • dist_fisher_f.qtf()
  • dist_fisher_f.isf()
  • dist_fisher_f.c_x()
  • dist_fisher_f.m_x()
  • dist_fisher_f.k_x()
  • dist_fisher_f.moments()
  • dist_fisher_f.cumulants()
  • dist_fisher_f.recurrence_pdf()
  • dist_fisher_f.recurrence_cdf()
• Boost: Student \(t\) (Pearson Type VII) distribution
  • Ctx.student_t_pdf()
  • Ctx.student_t_cdf()
  • Ctx.student_t_qtf()
  • ctx.dist_student_t
  • dist_student_t.pdf()
  • dist_student_t.cdf()
  • dist_student_t.sf()
  • dist_student_t.qtf()
  • dist_student_t.isf()
  • dist_student_t.c_x()
  • dist_student_t.m_x()
  • dist_student_t.k_x()
  • dist_student_t.moments()
  • dist_student_t.cumulants()
• Distribution of the negative logarithm of a beta variable
  • ctx.dist_logrv_beta
  • dist_logrv_beta.pdf()
  • dist_logrv_beta.cdf()
  • dist_logrv_beta.sf()
  • dist_logrv_beta.qtf()
  • dist_logrv_beta.isf()
  • dist_logrv_beta.c_x()
  • dist_logrv_beta.m_x()
  • dist_logrv_beta.k_x()
  • dist_logrv_beta.moments()
  • dist_logrv_beta.cumulants()
  • ctx.logrv_beta_ecf_pdf()
  • ctx.logrv_beta_ecf_qtf()
• Beta-prime (Pearson Type VI) distribution
  • ctx.dist_beta_prime
  • dist_beta_prime.pdf()
  • dist_beta_prime.cdf()
  • dist_beta_prime.sf()
  • dist_beta_prime.qtf()
  • dist_beta_prime.isf()
  • dist_beta_prime.c_x()
  • dist_beta_prime.m_x()
  • dist_beta_prime.k_x()
  • dist_beta_prime.moments()
  • dist_beta_prime.cumulants()
• Generalized Beta (Type 1) distribution
  • ctx.dist_genbeta1
  • dist_genbeta1.pdf()
  • dist_genbeta1.cdf()
  • dist_genbeta1.sf()
  • dist_genbeta1.qtf()
  • dist_genbeta1.isf()
  • dist_genbeta1.c_x()
  • dist_genbeta1.m_x()
  • dist_genbeta1.k_x()
  • dist_genbeta1.moments()
  • dist_genbeta1.cumulants()
• Generalized Beta (Type 2) distribution
  • ctx.dist_genbeta2
  • dist_genbeta2.pdf()
  • dist_genbeta2.cdf()
  • dist_genbeta2.sf()
  • dist_genbeta2.qtf()
  • dist_genbeta2.isf()
  • dist_genbeta2.c_x()
  • dist_genbeta2.m_x()
  • dist_genbeta2.k_x()
  • dist_genbeta2.moments()
  • dist_genbeta2.cumulants()
• Generalized logistic distribution (JKB Types I - IV)
  • ctx.dist_genlogistic
  • dist_genlogistic.pdf()
  • dist_genlogistic.cdf()
  • dist_genlogistic.sf()
  • dist_genlogistic.qtf()
  • dist_genlogistic.isf()
  • dist_genlogistic.c_x()
  • dist_genlogistic.m_x()
  • dist_genlogistic.k_x()
  • dist_genlogistic.moments()
  • dist_genlogistic.cumulants()
• Generalized beta-exponential distribution
  • ctx.dist_gen_beta_exp
  • dist_gen_beta_exp.pdf()
  • dist_gen_beta_exp.cdf()
  • dist_gen_beta_exp.sf()
  • dist_gen_beta_exp.qtf()
  • dist_gen_beta_exp.isf()
  • dist_gen_beta_exp.c_x()
  • dist_gen_beta_exp.m_x()
  • dist_gen_beta_exp.k_x()
  • dist_gen_beta_exp.moments()
  • dist_gen_beta_exp.cumulants()
• Feller-Pareto distribution
  • ctx.dist_feller_pareto
  • dist_feller_pareto.pdf()
  • dist_feller_pareto.cdf()
  • dist_feller_pareto.sf()
  • dist_feller_pareto.qtf()
  • dist_feller_pareto.isf()
  • dist_feller_pareto.c_x()
  • dist_feller_pareto.m_x()
  • dist_feller_pareto.k_x()
  • dist_feller_pareto.moments()
  • dist_feller_pareto.cumulants()
• Fisher \(z\) distribution
  • ctx.dist_fisher_z
  • dist_fisher_z.pdf()
  • dist_fisher_z.cdf()
  • dist_fisher_z.sf()
  • dist_fisher_z.qtf()
  • dist_fisher_z.isf()
  • dist_fisher_z.c_x()
  • dist_fisher_z.m_x()
  • dist_fisher_z.k_x()
  • dist_fisher_z.moments()
  • dist_fisher_z.cumulants()
  • ctx.fisher_z_ecf()
  • ctx.fisher_z_ecf_inv()
  • ctx.fisher_z_spa()
  • ctx.fisher_z_spa_inv()
• Skew t-distribution (Jones)
  • ctx.dist_skewt
  • dist_skewt.pdf()
  • dist_skewt.cdf()
  • dist_skewt.sf()
  • dist_skewt.qtf()
  • dist_skewt.isf()
  • dist_skewt.c_x()
  • dist_skewt.m_x()
  • dist_skewt.k_x()
  • dist_skewt.moments()
  • dist_skewt.cumulants()
• Pearson’s rho distribution (under \(H_0\))
  • ctx.dist_pearson_rho
  • dist_pearson_rho.pdf()
  • dist_pearson_rho.cdf()
  • dist_pearson_rho.sf()
  • dist_pearson_rho.qtf()
  • dist_pearson_rho.isf()
  • dist_pearson_rho.c_x()
  • dist_pearson_rho.m_x()
  • dist_pearson_rho.k_x()
  • dist_pearson_rho.moments()
  • dist_pearson_rho.cumulants()