Distributions related to multivariate statistical analysis

• Distribution of the sum of the negative logarithms of independent beta variables
  • ctx.dist_logrv_beta_sum
  • dist_logrv_beta_sum.pdf()
  • dist_logrv_beta_sum.cdf()
  • dist_logrv_beta_sum.sf()
  • dist_logrv_beta_sum.qtf()
  • dist_logrv_beta_sum.isf()
  • dist_logrv_beta_sum.c_x()
  • dist_logrv_beta_sum.m_x()
  • dist_logrv_beta_sum.k_x()
  • dist_logrv_beta_sum.moments()
  • dist_logrv_beta_sum.cumulants()
  • ctx.beta_product_ecf()
  • ctx.beta_product_ecf_inv()
• Distribution of the product of independent beta variables
  • ctx.dist_beta_product
  • dist_beta_product.pdf()
  • dist_beta_product.cdf()
  • dist_beta_product.sf()
  • dist_beta_product.qtf()
  • dist_beta_product.isf()
  • dist_beta_product.c_x()
  • dist_beta_product.m_x()
  • dist_beta_product.k_x()
  • dist_beta_product.moments()
  • dist_beta_product.cumulants()
  • ctx.log_beta_prod_gp()
  • ctx.beta_prod_spa()
  • ctx.beta_prod_spa_inv()
  • ctx.beta_product_bd()
  • ctx.beta_product_bd_inv()
  • ctx.beta_product_bd_cdf_old()
• Distribution of Wilks’ \(\Lambda\)
  • ctx.dist_wilks_lambda
  • dist_wilks_lambda.pdf()
  • dist_wilks_lambda.cdf()
  • dist_wilks_lambda.sf()
  • dist_wilks_lambda.qtf()
  • dist_wilks_lambda.isf()
  • dist_wilks_lambda.c_x()
  • dist_wilks_lambda.m_x()
  • dist_wilks_lambda.k_x()
  • dist_wilks_lambda.moments()
  • dist_wilks_lambda.cumulants()
  • ctx.wilks_lambda_gp()
  • ctx.wilks_lambda_ecf()
  • ctx.wilks_lambda_ecf_inv()
  • ctx.wilks_lambda_spa()
  • ctx.wilks_lambda_spa_inv()
  • ctx.wilks_lambda_bd()
    • ctx.wilks_lambda_bd_inv()
• Distribution of Wilks’ \(L_{vc}\)
  • ctx.dist_wilks_cs
  • dist_wilks_cs.pdf()
  • dist_wilks_cs.cdf()
  • dist_wilks_cs.sf()
  • dist_wilks_cs.qtf()
  • dist_wilks_cs.isf()
  • dist_wilks_cs.c_x()
  • dist_wilks_cs.m_x()
  • dist_wilks_cs.k_x()
  • dist_wilks_cs.moments()
  • dist_wilks_cs.cumulants()
• Distribution of Wilks’ \(L_{vcm}\)
  • ctx.dist_wilks_lcm
  • dist_wilks_lcm.pdf()
  • dist_wilks_lcm.cdf()
  • dist_wilks_lcm.sf()
  • dist_wilks_lcm.qtf()
  • dist_wilks_lcm.isf()
  • dist_wilks_lcm.c_x()
  • dist_wilks_lcm.m_x()
  • dist_wilks_lcm.k_x()
  • dist_wilks_lcm.moments()
  • dist_wilks_lcm.cumulants()
• Distribution of Wilks’ test of independence of \(p\) variates
  • ctx.dist_wilks_ip
  • dist_wilks_ip.pdf()
  • dist_wilks_ip.cdf()
  • dist_wilks_ip.sf()
  • dist_wilks_ip.qtf()
  • dist_wilks_ip.isf()
  • dist_wilks_ip.c_x()
  • dist_wilks_ip.m_x()
  • dist_wilks_ip.k_x()
  • dist_wilks_ip.moments()
  • dist_wilks_ip.cumulants()
• Distribution of Wilks’ test of independence of \(k\) groups of variates
  • ctx.dist_wilks_iblocks
  • dist_wilks_iblocks.pdf()
  • dist_wilks_iblocks.cdf()
  • dist_wilks_iblocks.sf()
  • dist_wilks_iblocks.qtf()
  • dist_wilks_iblocks.isf()
  • dist_wilks_iblocks.c_x()
  • dist_wilks_iblocks.m_x()
  • dist_wilks_iblocks.k_x()
  • dist_wilks_iblocks.moments()
  • dist_wilks_iblocks.cumulants()
  • ctx.wilks_iblocks_bd()
  • ctx.wilks_iblocks_bd_inv()
• Distribution of Mauchly’s test of sphericity vs general structure
  • ctx.dist_mauchley
  • dist_mauchley.pdf()
  • dist_mauchley.cdf()
  • dist_mauchley.sf()
  • dist_mauchley.qtf()
  • dist_mauchley.isf()
  • dist_mauchley.c_x()
  • dist_mauchley.m_x()
  • dist_mauchley.k_x()
  • dist_mauchley.moments()
  • dist_mauchley.cumulants()
  • ctx.mauchley_bd()
  • ctx.mauchley_bd_inv()
• Distribution of Box’s test of equality of covariance matrices, equal sample sizes
  • ctx.dist_box_nsame_cov
  • dist_box_nsame_cov.pdf()
  • dist_box_nsame_cov.cdf()
  • dist_box_nsame_cov.sf()
  • dist_box_nsame_cov.qtf()
  • dist_box_nsame_cov.isf()
  • dist_box_nsame_cov.c_x()
  • dist_box_nsame_cov.m_x()
  • dist_box_nsame_cov.k_x()
  • dist_box_nsame_cov.moments()
  • dist_box_nsame_cov.cumulants()
  • ctx.box_spa()
  • ctx.box_spa_inv()
• Distribution of Box’s test of equality of k covariance matrices, unequal sample sizes
  • ctx.dist_box_cov
  • dist_box_cov.pdf()
  • dist_box_cov.cdf()
  • dist_box_cov.sf()
  • dist_box_cov.qtf()
  • dist_box_cov.isf()
  • dist_box_cov.c_x()
  • dist_box_cov.m_x()
  • dist_box_cov.k_x()
  • dist_box_cov.moments()
  • dist_box_cov.cumulants()
  • ctx.log_box_cov_gp()
  • ctx.box_davis_ecf()
  • ctx.box_davis_ecf_inv()
  • ctx.box_cov_bd()
  • ctx.box_cov_bd_inv()
• Distribution of Box’s test for same multivariate normal distributions, unequal sample sizes
  • ctx.dist_box_mvn
  • dist_box_mvn.pdf()
  • dist_box_mvn.cdf()
  • dist_box_mvn.sf()
  • dist_box_mvn.qtf()
  • dist_box_mvn.isf()
  • dist_box_mvn.c_x()
  • dist_box_mvn.m_x()
  • dist_box_mvn.k_x()
  • dist_box_mvn.moments()
  • dist_box_mvn.cumulants()
  • ctx.box_means_cov_bd()
  • ctx.box_means_cov_bd_inv()
• Distribution of the modified likelihood ratio test (LRT) for a given covariance matrix
  • ctx.dist_lrt_s0
  • dist_lrt_s0.pdf()
  • dist_lrt_s0.cdf()
  • dist_lrt_s0.sf()
  • dist_lrt_s0.qtf()
  • dist_lrt_s0.isf()
  • dist_lrt_s0.c_x()
  • dist_lrt_s0.m_x()
  • dist_lrt_s0.k_x()
  • dist_lrt_s0.moments()
  • dist_lrt_s0.cumulants()
  • ctx.lrt_vc0_bd()
  • ctx.lrt_vc0_bd_inv()
• Distribution of the modified likelihood ratio test (LRT) for a given covariance matrix and mean vector
  • ctx.dist_lrt_x0_s0
  • dist_lrt_x0_s0.pdf()
  • dist_lrt_x0_s0.cdf()
  • dist_lrt_x0_s0.sf()
  • dist_lrt_x0_s0.qtf()
  • dist_lrt_x0_s0.isf()
  • dist_lrt_x0_s0.c_x()
  • dist_lrt_x0_s0.m_x()
  • dist_lrt_x0_s0.k_x()
  • dist_lrt_x0_s0.moments()
  • dist_lrt_x0_s0.cumulants()
  • ctx.lrt_x0_vc0_bd()
  • ctx.lrt_x0_vc0_bd_inv()
• Central distribution of Roy’s largest root
  • ctx.dist_roy
  • dist_roy.pdf()
  • dist_roy.cdf()
  • dist_roy.sf()
  • dist_roy.qtf()
  • dist_roy.isf()
  • dist_roy.c_x()
  • dist_roy.m_x()
  • dist_roy.k_x()
  • dist_roy.moments()
  • dist_roy.cumulants()
• Central distribution of Pillai’s \(V\)
  • ctx.dist_pillai_v
  • dist_pillai_v.pdf()
  • dist_pillai_v.cdf()
  • dist_pillai_v.sf()
  • dist_pillai_v.qtf()
  • dist_pillai_v.isf()
  • dist_pillai_v.c_x()
  • dist_pillai_v.m_x()
  • dist_pillai_v.k_x()
  • dist_pillai_v.moments()
  • dist_pillai_v.cumulants()
  • ctx.pillai_v_ecf()
  • ctx.pillai_v_ecf_inv()
  • ctx.pillai_v_bd()
  • ctx.pillai_v_bd_inv()
• Central distribution of Hotelling’s \(T^2\)
  • ctx.dist_hotelling_t2
  • dist_hotelling_t2.pdf()
  • dist_hotelling_t2.cdf()
  • dist_hotelling_t2.sf()
  • dist_hotelling_t2.qtf()
  • dist_hotelling_t2.isf()
  • dist_hotelling_t2.c_x()
  • dist_hotelling_t2.m_x()
  • dist_hotelling_t2.k_x()
  • dist_hotelling_t2.moments()
  • dist_hotelling_t2.cumulants()
  • ctx.hotelling_t2_ecf()
  • ctx.hotelling_t2_ecf_inv()
  • ctx.hotelling_t2_bd()
  • ctx.hotelling_t2_bd_inv()
• Noncentral Distribution of Wilks’ \(\Lambda\): MANOVA
  • ctx.dist_wilks_lambda_glm
  • dist_wilks_lambda_glm.pdf()
  • dist_wilks_lambda_glm.cdf()
  • dist_wilks_lambda_glm.sf()
  • dist_wilks_lambda_glm.qtf()
  • dist_wilks_lambda_glm.isf()
  • dist_wilks_lambda_glm.c_x()
  • dist_wilks_lambda_glm.m_x()
  • dist_wilks_lambda_glm.k_x()
  • dist_wilks_lambda_glm.moments()
  • dist_wilks_lambda_glm.cumulants()
  • ctx.wilks_lambda_glm_gp()
  • ctx.wilks_lambda_glm_spa()
  • ctx.wilks_lambda_glm_inv()
• Noncentral Distribution of Wilks’ \(\Lambda\): Canonical Correlation
  • ctx.dist_wilks_lambda_corr
  • dist_wilks_lambda_corr.pdf()
  • dist_wilks_lambda_corr.cdf()
  • dist_wilks_lambda_corr.sf()
  • dist_wilks_lambda_corr.qtf()
  • dist_wilks_lambda_corr.isf()
  • dist_wilks_lambda_corr.c_x()
  • dist_wilks_lambda_corr.m_x()
  • dist_wilks_lambda_corr.k_x()
  • dist_wilks_lambda_corr.moments()
  • dist_wilks_lambda_corr.cumulants()
  • ctx.wilks_lambda_ind_gp()
  • ctx.wilks_lambda_ind_spa()
  • ctx.wilks_lambda_ind_spa_inv()