!g5@dZddlZddlmZddlmZddZddZddZ y) zM Created on Mon Oct 5 12:36:54 2020 Author: Josef Perktold License: BSD-3 N)special)Holderc F|dz }||z }tj|d}tj|||dzz }tj||dz|dzz }tj||d}tj||d|z |g} t || ||||d} | S)uwnoncentrality parameter for chi-square statistic `nc` is zero-truncated umvue Parameters ---------- chi2_stat : float Chisquare-statistic, for example from a hypothesis test df : int or float Degrees of freedom alpha : float in (0, 1) Significance level for the confidence interval, covarage is 1 - alpha. Returns ------- HolderTuple The main attributes are - ``nc`` : estimate of noncentrality parameter - ``confint`` : lower and upper bound of confidence interval for `nc`` Other attributes are estimates for nc by different methods. References ---------- .. [1] Kubokawa, T., C.P. Robert, and A.K.Md.E. Saleh. 1993. “Estimation of Noncentrality Parameters.” Canadian Journal of Statistics 21 (1): 45–57. https://doi.org/10.2307/3315657. .. [2] Li, Qizhai, Junjian Zhang, and Shuai Dai. 2009. “On Estimating the Non-Centrality Parameter of a Chi-Squared Distribution.” Statistics & Probability Letters 79 (1): 98–104. https://doi.org/10.1016/j.spl.2008.07.025. r?z7Noncentrality for chisquare-distributed random variable)ncconfintnc_umvuenc_lzdnc_krs nc_medianname)npmaximumr chndtrincr) chi2_statdfalpha alpha_halfr r r r rciress Z/var/www/dash_apps/app1/venv/lib/python3.12/site-packages/statsmodels/stats/effect_size.py_noncentrality_chisquarer sJJ2~H Ha B ZZ)rAv"6 7F ZZ)a-26": ;F!!)R5I   9b1z>:*F GB B"$O  C Jc8|dz }||z|z }|dz |z|z }tj|d}tj||dz|dz z|dzz }tj||d|} tj||d|z |g|} t || ||| d} | S)uYnoncentrality parameter for f statistic `nc` is zero-truncated umvue Parameters ---------- fstat : float f-statistic, for example from a hypothesis test df : int or float Degrees of freedom alpha : float in (0, 1) Significance level for the confidence interval, covarage is 1 - alpha. Returns ------- HolderTuple The main attributes are - ``nc`` : estimate of noncentrality parameter - ``confint`` : lower and upper bound of confidence interval for `nc`` Other attributes are estimates for nc by different methods. References ---------- .. [1] Kubokawa, T., C.P. Robert, and A.K.Md.E. Saleh. 1993. “Estimation of Noncentrality Parameters.” Canadian Journal of Statistics 21 (1): 45–57. https://doi.org/10.2307/3315657. rrrrz/Noncentrality for F-distributed random variable)r r r r rr)rrr ncfdtrincr) f_statdf1df2rrx_sr r r rrrs r_noncentrality_fr"Fs<J 3, Ca3$H Ha B ZZ#'S1W"5q"A BF!!#sC8I   3a*nj%A6 JB B"$G  C Jrcb|dz }tjtj|dz dz tj|dz z }tj|dz |z}||z }tj |d|}tj |d|z |g|}t |||d} | S)uRnoncentrality parameter for t statistic Parameters ---------- fstat : float f-statistic, for example from a hypothesis test df : int or float Degrees of freedom alpha : float in (0, 1) Significance level for the confidence interval, covarage is 1 - alpha. Returns ------- HolderTuple The main attributes are - ``nc`` : estimate of noncentrality parameter - ``confint`` : lower and upper bound of confidence interval for `nc`` Other attributes are estimates for nc by different methods. References ---------- .. [1] Hedges, Larry V. 2016. “Distribution Theory for Glass’s Estimator of Effect Size and Related Estimators:” Journal of Educational Statistics, November. https://doi.org/10.3102/10769986006002107. rg@rrz/Noncentrality for t-distributed random variable)r r rr)rexprgammalnsqrt nctdtrincr) t_statrrrgfacc11r rrrs r_noncentrality_tr+ws<J 66'//"R%),wr"u/EE FD ''"R%.4 C #B!!"c62I   2J ;V DB B$G C Jr)g?) __doc__numpyrscipyrstatsmodels.stats.baserrr"r+rrr1s&)6r.b+r