python - Calculating Integral of a linear function with respect to a lognormal distributed variable accurately -

-

i iteratively calculate fixed point of following functional equation:

enter image description here

where h know function , q lognormal distribution. let f* function solving functional equation. know f(z)/z constant. when calculating f numerically python ratio f*(z)/z monotonically increasing. quantify magnitude of error, calculate difference between last , first point of ratio. think source of problem stems numerical integration of function f:

the integral on function f taken respect lognormal distribution stdv sigma , mean zero. numerically, calculate integral follows: 

integrand = lambda z: f(z) * phi.pdf(z) result, error = fixed_quad(integrand, int_min, int_max, n=120)

the error calculate determined integration bounds int_min , int_max. initially, specify integration bounds be:

int_min, int_max = np.exp( - 1 * sigma), np.exp( 1 * sigma)

however, when change integration bounds cover 95% of probability mass of lognormal distribution, i.e:

int_min, int_max = np.exp( - 2 * sigma), np.exp( 2 * sigma)

the difference between highest , lowest point in ratio f*(z)/z increases factor 100. numerical value stdv sigma = 0.012.

there 2 comments want make before stating question:

  1. when use function scipy.quadrature instead of scipy.fixed_quad , define error tolerance integration around 1e-8 (the default value of scipy.quadrature), difference between highest , lowest point in ratio not change. indicate integration procedure not source of problem after all?
  2. the level of solution f* depends heavily on integration bounds. level increases factor 3. change of levels might related following question posted on stackoverlow: discontinuity in results when using scipy.integrate.quad

what other effect changing integration bounds might have 1 accuracy of solution f*? if integration routine used can indeed cause problem, there better way calculate integral numerically?


Comments

Post a Comment

Popular posts from this blog

python - mat is not a numerical tuple : openCV error -

-
i have write down code showing error ma not getting it: please help: showing mat not numerical tuple: import cv import cv2 capture = cv2.videocapture("j.3gp") while(1): _, frame1 = capture.read() grayimage1 = cv2.cvtcolor(frame1, cv2.color_bgr2gray) _, frame2 = capture.read() grayimage2 = cv2.cvtcolor(frame2, cv2.color_bgr2gray) differenceimage = cv2.absdiff(grayimage1,grayimage2) thresholdimage = cv2.threshold(differenceimage,25,255,cv2.thresh_binary) cv2.imshow("difference image", differenceimage) cv2.imshow("threshold image", thresholdimage) cv2.imshow("image", frame1) k = cv2.waitkey(30) & 0xff error arising : ----------------------------------------------------------------------------------------- traceback (most recent call last): file "desk.py", line 15, in <module> cv2.imshow("threshold image", thresholdimage) typeerror: mat not numerical tuple
Read more

c# - MSAA finds controls UI Automation doesn't -

-
i'm working on automating windows application. i'm using teststack white framework. i've hit problem. program has 'window' object cannot see inside of. white shows no controls inside of it. inspect.exe shows no controls inside of either when running in ui automation mode. if switch inspect msaa see controls inside fine. there anyway me use msaa c# handle on these controls? if can identify msaa functions need, can use p/invoke call them c#. here's example article doing msaa: http://www.codeproject.com/articles/38906/ui-automation-using-microsoft-active-accessibility also, pinvoke.net can used identify iaccessible (msaa) functions: http://www.pinvoke.net/search.aspx?search=iaccessible&namespace=[all] here's answer along lines: msaa com-based? finally, alternative p/invoke, might able use tlbimp.exe create wrapper assembly oleacc.dll, , access msaa functions through it. i'm not sure if works msaa, it's worth try. as e
Read more

wordpress - .htaccess: RewriteRule: bad flag delimiters -

-
pulling hair out on one. have following .htaccess file custom redirects in addition wordpress's default settings. when tested on local wamp server worked fine after moving production i'm not getting rewriterule: bad flag delimiters error in server log , after while site goes down internal server error any appreciated. in advance! <ifmodule mod_rewrite.c> rewriteengine on rewritebase / rewriterule ^rockford_weddings___welcome\.html$ /wedding/ [r=301,l] rewriterule ^blog/?$ /journal/ [r=301,l] rewriterule ^blog/(.*)$ /$1 [r=301,l] rewriterule ^portraitinvestment/?$ /portraitinvestment\.pdf [r=301,l] rewriterule ^weddinginvestment/?$ /weddinginvestment\.pdf [r=301,l] rewriterule ^holidaycards2014/?$ /holidaycards2014\.pdf [r=301,l] </ifmodule> # begin wordpress <ifmodule mod_rewrite.c> rewriteengine on rewritebase / rewriterule ^index\.php$ - [l] rewritecond %{request_filename} !-f rewritecond %{request_filename} !-d rewriterule . /index.php [l] </
Read more