Ph'addlZddlmZddlmZddlmZmZm Z m Z m Z m Z m Z mZmZmZmZmZmZmZmZmZmZmZddZdZdZdZd Zd Zd Zd Z d Z!dZ"dZ#dZ$dZ%dZ&dZ'dZ(dZ)dZ*dZ+y)N)assert_allclosefmin) CensoredDatabetacauchychi2expongammagumbel_lgumbel_rinvgauss invweibulllaplacelogisticlognormnctncx2norm weibull_max weibull_minc$t||||ddS)Ng-q=)argsdispxtolftolr)funcx0rrs yC:\Users\daisl\Desktop\realtime-object-detection\venv\Lib\site-packages\scipy/stats/tests/test_continuous_fit_censored.py optimizerr s bt$U GGctddgddgddgddgg }tj|d d t \}}}}t |d dt |dd|d k(sJ|d k(sJy)a Test fitting beta shape parameters to interval-censored data. Calculation in R: > library(fitdistrplus) > data <- data.frame(left=c(0.10, 0.50, 0.75, 0.80), + right=c(0.20, 0.55, 0.90, 0.95)) > result = fitdistcens(data, 'beta', control=list(reltol=1e-14)) > result Fitting of the distribution ' beta ' on censored data by maximum likelihood Parameters: estimate shape1 1.419941 shape2 1.027066 > result$sd shape1 shape2 0.9914177 0.6866565 皙?皙??皙???皙?ffffff?intervalrflocfscaler g ?h㈵>rtolg*V n?N)rrfitr r)dataablocscales r test_betar:s|* 4,#',#',#',"0 1D xx1Q)LAq#uAxd+Axd+ !8O8 A::r!ctddgdg}tj|t\}}t |ddt |d dy ) a Test fitting the Cauchy distribution to right-censored data. Calculation in R, with two values not censored [1, 10] and one right-censored value [30]. > library(fitdistrplus) > data <- data.frame(left=c(1, 10, 30), right=c(1, 10, NA)) > result = fitdistcens(data, 'cauchy', control=list(reltol=1e-14)) > result Fitting of the distribution ' cauchy ' on censored data by maximum likelihood Parameters: estimate location 7.100001 scale 7.455866 r- ) uncensoredrightr g}if@r1r2gne@Nrrr4r rr5r8r9s rtest_cauchy_right_censoredrC5sB$ Ar72$ 7DDI6JCCt,E8$/r!ctddgdgdgddgg}tj|t\}}t |dd t |d d y ) a\ Test fitting the Cauchy distribution to data with mixed censoring. Calculation in R, with: * two values not censored [1, 10], * one left-censored [1], * one right-censored [30], and * one interval-censored [[4, 8]]. > library(fitdistrplus) > data <- data.frame(left=c(NA, 1, 4, 10, 30), right=c(1, 1, 8, 10, NA)) > result = fitdistcens(data, 'cauchy', control=list(reltol=1e-14)) > result Fitting of the distribution ' cauchy ' on censored data by maximum likelihood Parameters: estimate location 4.605150 scale 5.900852 r-r<r=r>leftr?r,r@g qk@r1r2g%Zx@NrArBs rtest_cauchy_mixedrIMsQ* Ar7!RD#$a& +DDI6JCC-E8$/r!ctddgdgdgddgg}tj|ddt\}}}t |d d |dk(sJ|dk(sJy ) a= Test fitting just the shape parameter (df) of chi2 to mixed data. Calculation in R, with: * two values not censored [1, 10], * one left-censored [1], * one right-censored [30], and * one interval-censored [[4, 8]]. > library(fitdistrplus) > data <- data.frame(left=c(NA, 1, 4, 10, 30), right=c(1, 1, 8, 10, NA)) > result = fitdistcens(data, 'chisq', control=list(reltol=1e-14)) > result Fitting of the distribution ' chisq ' on censored data by maximum likelihood Parameters: estimate df 5.060329 r-r<r=rErFrGrr.ge=@r1r2N)rr r4r r)r5dfr8r9s rtest_chi2_mixedrLisb( Ar7!RD#$a& +DXXd1 JNBUBt, !8O8 A::r!cdgd}dgdzdgdzz}tj||}tj|dt\}}|dk(sJt ||j z }|jj|jjz}||z }t||dy ) a For the exponential distribution with loc=0, the exact solution for fitting n uncensored points x[0]...x[n-1] and m right-censored points x[n]..x[n+m-1] is scale = sum(x)/n That is, divide the sum of all the values (not censored and right-censored) by the number of uncensored values. (See, for example, https://en.wikipedia.org/wiki/Censoring_(statistics)#Likelihood.) The second derivative of the log-likelihood function is n/scale**2 - 2*sum(x)/scale**3 from which the estimate of the standard error can be computed. ----- Calculation in R, for reference only. The R results are not used in the test. > library(fitdistrplus) > dexps <- function(x, scale) { + return(dexp(x, 1/scale)) + } > pexps <- function(q, scale) { + return(pexp(q, 1/scale)) + } > left <- c(1, 2.5, 3, 6, 7.5, 10, 12, 12, 14.5, 15, + 16, 16, 20, 20, 21, 22) > right <- c(1, 2.5, 3, 6, 7.5, 10, 12, 12, 14.5, 15, + NA, NA, NA, NA, NA, NA) > result = fitdistcens(data, 'exps', start=list(scale=mean(data$left)), + control=list(reltol=1e-14)) > result Fitting of the distribution ' exps ' on censored data by maximum likelihood Parameters: estimate scale 19.85 > result$sd scale 6.277119 )r-@g@r< rQg-@rSrTFr<TrPrr/r g:0yE>N) rright_censoredr r4r len num_censored _uncensoredsum_rightr)obscensr5r8r9ntotalexpecteds rtest_expon_right_censoredrcs\ LC 72:q D  & &sD 1D4a9=JC !8O8 D D%%''A    "T[[__%6 6EqyHE8T*r!ctjgddgdzdgz}tj|dt\}}}t |dd|dk(sJt |d dy ) a Fit gamma shape and scale to data with one right-censored value. Calculation in R: > library(fitdistrplus) > data <- data.frame(left=c(2.5, 2.9, 3.8, 9.1, 9.3, 12.0, 23.0, 25.0), + right=c(2.5, 2.9, 3.8, 9.1, 9.3, 12.0, 23.0, NA)) > result = fitdistcens(data, 'gamma', start=list(shape=1, scale=10), + control=list(reltol=1e-13)) > result Fitting of the distribution ' gamma ' on censored data by maximum likelihood Parameters: estimate shape 1.447623 scale 8.360197 > result$sd shape scale 0.7053086 5.1016531 )rNg333333@gffffff@g333333"@g"@g(@g7@g9@rr-rWgv)?r1r2g library(evd) > library(fitdistrplus) > data = data.frame(left=c(0, 2, 3, 9, 10, 10), + right=c(1, 2, 3, 9, NA, NA)) > result = fitdistcens(data, 'gumbel', + control=list(reltol=1e-14), + start=list(loc=4, scale=5)) > result Fitting of the distribution ' gumbel ' on censored data by maximum likelihood Parameters: estimate loc 4.487853 scale 4.843640 rO r<rr-)r?r,r@g@r1r2gc*_@N)rHr,g)nparrayrr r4r rr ) r>r?r,r5r8r9data2loc2scale2s r test_gumbelrrs,)$J HHb"X Exx!Q!H  %( CDdi8JCC-E8$/ *E6#+AttG#4"4 6E<<;LD&D)$/FH40r!c,gd}t|dgdg}tj|ddt\}}}t |dd |dk(sJ|dk(sJtj|dt \}}}t |d d |dk(sJt |d d y)a Fit just the shape parameter of invgauss to data with one value left-censored and one value right-censored. Calculation in R; using a fixed dispersion parameter amounts to fixing the scale to be 1. > library(statmod) > library(fitdistrplus) > left <- c(NA, 0.4813096, 0.5571880, 0.5132463, 0.3801414, 0.5904386, + 0.4822340, 0.3478597, 3, 0.7191797, 1.5810902, 0.4442299) > right <- c(0.15, 0.4813096, 0.5571880, 0.5132463, 0.3801414, 0.5904386, + 0.4822340, 0.3478597, NA, 0.7191797, 1.5810902, 0.4442299) > data <- data.frame(left=left, right=right) > result = fitdistcens(data, 'invgauss', control=list(reltol=1e-12), + fix.arg=list(dispersion=1), start=list(mean=3)) > result Fitting of the distribution ' invgauss ' on censored data by maximum likelihood Parameters: estimate mean 0.853469 Fixed parameters: value dispersion 1 > result$sd mean 0.247636 Here's the R calculation with the dispersion as a free parameter to be fit. > result = fitdistcens(data, 'invgauss', control=list(reltol=1e-12), + start=list(mean=3, dispersion=1)) > result Fitting of the distribution ' invgauss ' on censored data by maximum likelihood Parameters: estimate mean 0.8699819 dispersion 1.2261362 The parametrization of the inverse Gaussian distribution in the `statmod` package is not the same as in SciPy (see https://arxiv.org/abs/1603.06687 for details). The translation from R to SciPy is scale = 1/dispersion mu = mean * dispersion > 1/result$estimate['dispersion'] # 1/dispersion dispersion 0.8155701 > result$estimate['mean'] * result$estimate['dispersion'] mean 1.066716 Those last two values are the SciPy scale and shape parameters. ) g ?g ({?gL`)l?g 6rHr?rr-r.g\d8O?g-C6 ?r2rWgBD?g cw&?N)rrr4r r)rfr5mur8r9s r test_invgaussrv sz A 1D6! =D\\$QqINNBUBt, !8O8 A::\\$Q)DNBUBt, !8O8E940r!ctgdddgddgg}tj|dt\}}}t |dd |dk(sJt |d d y ) a Fit invweibull to censored data. Here is the calculation in R. The 'frechet' distribution from the evd package matches SciPy's invweibull distribution. The `loc` parameter is fixed at 0. > library(evd) > library(fitdistrplus) > data = data.frame(left=c(0, 2, 3, 9, 10, 10), + right=c(1, 2, 3, 9, NA, NA)) > result = fitdistcens(data, 'frechet', + control=list(reltol=1e-14), + start=list(loc=4, scale=5)) > result Fitting of the distribution ' frechet ' on censored data by maximum likelihood Parameters: estimate scale 2.7902200 shape 0.6379845 Fixed parameters: value loc 0 rir<rr-r>r?r,rWgp[[x^j?r1r2g5)^R@N)rrr4r r)r5cr8r9s rtest_invweibullrz^sZ8 9RH#$a& +DNN4a9EMAsEAyt, !8O8E940r!ctjgd}||dk7|dk7z}||dk(}||dk(}t|||}tj|ddt \}}t |dd t |d d y ) a Fir the Laplace distribution to left- and right-censored data. Calculation in R: > library(fitdistrplus) > dlaplace <- function(x, location=0, scale=1) { + return(0.5*exp(-abs((x - location)/scale))/scale) + } > plaplace <- function(q, location=0, scale=1) { + z <- (q - location)/scale + s <- sign(z) + f <- -s*0.5*exp(-abs(z)) + (s+1)/2 + return(f) + } > left <- c(NA, -41.564, 50.0, 15.7384, 50.0, 10.0452, -2.0684, + -19.5399, 50.0, 9.0005, 27.1227, 4.3113, -3.7372, + 25.3111, 14.7987, 34.0887, 50.0, 42.8496, 18.5862, + 32.8921, 9.0448, -27.4591, NA, 19.5083, -9.7199) > right <- c(-50.0, -41.564, NA, 15.7384, NA, 10.0452, -2.0684, + -19.5399, NA, 9.0005, 27.1227, 4.3113, -3.7372, + 25.3111, 14.7987, 34.0887, NA, 42.8496, 18.5862, + 32.8921, 9.0448, -27.4591, -50.0, 19.5083, -9.7199) > data <- data.frame(left=left, right=right) > result <- fitdistcens(data, 'laplace', start=list(location=10, scale=10), + control=list(reltol=1e-13)) > result Fitting of the distribution ' laplace ' on censored data by maximum likelihood Parameters: estimate location 14.79870 scale 30.93601 > result$sd location scale 0.1758864 7.0972125 )Igx&1DI@gz/@r}gSt$$@g_LgC63r}gK7A"@g8gDi;@g\m>@g g?O9@b4-@gޓZ A@r}g?W[lE@gK42@g|a2U0r@@g"@gݓu;r|g3@gǘp#r|2r}rtr<r8r9r r~r1r2gY>@N)rmrnrrr4r r)r^rfrHr?r5r8r9s r test_laplacersN ((H IC SE\cRi ()A se| D t E 14u =DTryIJCC-E8$/r!ctjgd}tj||dk(}t j |t \}}t|ddt|dd y ) a Fit the logistic distribution to left-censored data. Calculation in R: > library(fitdistrplus) > left = c(13.5401, 37.4235, 11.906 , 13.998 , NA , 0.4023, NA , + 10.9044, 21.0629, 9.6985, NA , 12.9016, 39.164 , 34.6396, + NA , 20.3665, 16.5889, 18.0952, 45.3818, 35.3306, 8.4949, + 3.4041, NA , 7.2828, 37.1265, 6.5969, 17.6868, 17.4977, + 16.3391, 36.0541) > right = c(13.5401, 37.4235, 11.906 , 13.998 , 0. , 0.4023, 0. , + 10.9044, 21.0629, 9.6985, 0. , 12.9016, 39.164 , 34.6396, + 0. , 20.3665, 16.5889, 18.0952, 45.3818, 35.3306, 8.4949, + 3.4041, 0. , 7.2828, 37.1265, 6.5969, 17.6868, 17.4977, + 16.3391, 36.0541) > data = data.frame(left=left, right=right) > result = fitdistcens(data, 'logis', control=list(reltol=1e-14)) > result Fitting of the distribution ' logis ' on censored data by maximum likelihood Parameters: estimate location 14.633459 scale 9.232736 > result$sd location scale 2.931505 1.546879 )g#+@g|?5B@gZd;'@g"+@g:H?rg;M %@g65@gʡe#@rg%䃞)@gEC@gBiQA@rg]4@gI&–0@gF_2@gpΈްF@g_QA@gec @gAǘ; @rg6r2g&4I,)w"@r1N)rmrnr left_censoredrr4r r)rfr5r8r9s r test_logisticrs[<  A  % %a16 ;Ddi8JCC.E8$/r!cgd}tj|dgdzzdgt|zdgdzz}tj|d\}}}|dk(sJt j |}t|dd t|d d y ) a# Ref: https://math.montana.edu/jobo/st528/documents/relc.pdf The data is the locomotive control time to failure example that starts on page 8. That's the 8th page in the PDF; the page number shown in the text is 270). The document includes SAS output for the data. )%g6@gB@gG@g@H@gI@gJ@g@K@gL@gP@gQ@g`Q@g S@g@S@gS@gT@g`T@gT@gT@gU@gV@g`W@gY@gZ@g [@g \@g`\@g]@g@]@g]@g]@g^@g^@g^@g_@g``@g`@g`@;rr-r/g3w@Mb@?r2g~jt?g{Gzt?N)rrXrYrr4rmlogr) miles_to_failr5sigmar8r9rus r test_lognormrs*M  & &}uRx'?()s3}+='=B'F HD Dq1E3 !8O8 BBT*E6-r!c&tjgdgd}tjd5t j |ddt \}}}}dddtd d td d dk(sJdk(sJy#1swY4xYw) a  Test fitting the noncentral t distribution to censored data. Calculation in R: > library(fitdistrplus) > data <- data.frame(left=c(1, 2, 3, 5, 8, 10, 25, 25), + right=c(1, 2, 3, 5, 8, 10, NA, NA)) > result = fitdistcens(data, 't', control=list(reltol=1e-14), + start=list(df=1, ncp=2)) > result Fitting of the distribution ' t ' on censored data by maximum likelihood Parameters: estimate df 0.5432336 ncp 2.8893565 )r-rjrOrFr<r)rrrrrrr-r-ignoreoverrr-r.NgBn+b?r1r2gTf@)rrXrmerrstaterr4r r)r5rKncr8r9s rtest_nctrs&  & &'B'? AD ( # WWT!/8:BU $B -B - !8O8 A:: $ #s #BBctgdddgddgg}tjd5tj|dd t \}}}}d d d t d d t dd dk(sJd k(sJy #1swY4xYw)a Test fitting the shape parameters (df, ncp) of ncx2 to mixed data. Calculation in R, with * 5 not censored values [2.7, 0.2, 6.5, 0.4, 0.1], * 1 interval-censored value [[0.6, 1.0]], and * 2 right-censored values [8, 8]. > library(fitdistrplus) > data <- data.frame(left=c(2.7, 0.2, 6.5, 0.4, 0.1, 0.6, 8, 8), + right=c(2.7, 0.2, 6.5, 0.4, 0.1, 1.0, NA, NA)) > result = fitdistcens(data, 'chisq', control=list(reltol=1e-14), + start=list(df=1, ncp=2)) > result Fitting of the distribution ' chisq ' on censored data by maximum likelihood Parameters: estimate df 1.052871 ncp 2.362934 )g@r$g@g?r#rFg333333?g?rxrrrr-r.NgQB?r1r2g I@)rrmrrr4r r)r5rKncpr8r9s r test_ncx2rs, # library(fitdistrplus) > data <- data.frame(left=c(0.10, 0.50, 0.75, 0.80), + right=c(0.20, 0.55, 0.90, 0.95)) > result = fitdistcens(data, 'norm', control=list(reltol=1e-14)) > result Fitting of the distribution ' norm ' on censored data by maximum likelihood Parameters: estimate mean 0.5919990 sd 0.2868042 > result$sd mean sd 0.1444432 0.1029451 r#r$r%r&r'r(r)r*r+r@gux?r1r2g[?N)rrr4r rrBs r test_normr>s\* 4,#',#',#',"0 1D $)4JCC.E940r!c Rd}t|jdDcgc]}|jdc}Dcgc]}t|dt|dk(f c}\}}t j ||}t j|d\}}}t|dd |dk(sJt|d d t jtj| |} tj| d\} } } t| dd | dk(sJt| d d ycc}wcc}w) Nz>3,5,6*,8,10*,11*,15,20*,22,23,27*,29,32,35,40,26,28,33*,21,24*,*rrjrgx&1@gMbP?r2g= ףp<@) zipsplitfloatrYrrXrr4rrrmrnr) swttimesr_r5ryr8r9roc2rprqs rtest_weibull_censored1r^s IA89 !E 1!''#, !EG!EAqtc!fk2!EGHKE4  & &ud 3DOODq1MAsEAu4( !8O8E5t,  & &'7 >E"u15BfBD) 199FE-'"FGs D#D$c|d}tj|jDcgc] }t|c}j ddj \}}|dz }t j||}tj|dt\}}}t|dd t|d d |dk(sJycc}w) Na 450 0 460 1 1150 0 1150 0 1560 1 1600 0 1660 1 1850 1 1850 1 1850 1 1850 1 1850 1 2030 1 2030 1 2030 1 2070 0 2070 0 2080 0 2200 1 3000 1 3000 1 3000 1 3000 1 3100 0 3200 1 3450 0 3750 1 3750 1 4150 1 4150 1 4150 1 4150 1 4300 1 4300 1 4300 1 4300 1 4600 0 4850 1 4850 1 4850 1 4850 1 5000 1 5000 1 5000 1 6100 1 6100 0 6100 1 6100 1 6300 1 6450 1 6450 1 6700 1 7450 1 7800 1 7800 1 8100 1 8100 1 8200 1 8500 1 8500 1 8500 1 8750 1 8750 0 8750 1 9400 1 9900 1 10100 1 10100 1 10100 1 11500 1 rlrjg@@rrWga4?g-C6?r2gsK:@gh㈵>) rmrnrintreshapeTrrXrr4r r)textrlifer_r5ryr8r9s rtest_weibull_min_sas1r{s  D"4::<8D  & &taS#d)a--@A3q5-H IDOOD!C.79MAsEAvD)Cd+E6-r!)r),numpyrm numpy.testingrscipy.optimizer scipy.statsrrrr r r r r rrrrrrrrrrr r:rCrIrLrcrgrrrvrzrrrrrrrrrrr!rrs)&&&&&H F00088;+|0D%1PN1b!1H10h&0R.>>B1@.:B.r!