python - Custom PDF from scipy.stats.rv_continuous unwanted upper-bound -


i attempting generate random probability density function of qso's of luminosity form:

1/( (l/l_b^* )^alpha + (l/l_b^* )^beta )

where l_b^*, alpha, , beta constants. this, following code used: 

import scipy.stats st  loglbreak = 43.88 alpha = 3.4 beta = 1.6   class my_pdf(st.rv_continuous):      def _pdf(self,l_l):          #"l_l" in log l                 l = 10**(l_l/loglbreak)         d = 1/(l**alpha + l**beta)         return d  dist_log_l = my_pdf(momtype = 0, = 0,name='l_l_dist')   distro = dist_log_l.rvs(size = 10000)

(l/l^* rased power of 10 since being done in log scale)

the distribution supposed produce graph approximates this, trailing off infinity, in reality graph produces looks this (10,000 samples). upper bound same regardless of amount of samples used. there reason being restricted in way is?

your pdf not normalized. integral of pdf on domain must 1. pdf integrates approximately 3.4712:

in [72]: scipy.integrate import quad  in [73]: quad(dist_log_l._pdf, 0, 100) out[73]: (3.4712183965415373, 2.0134487716044682e-11)  in [74]: quad(dist_log_l._pdf, 0, 800) out[74]: (3.4712184965748905, 2.013626296581202e-11)  in [75]: quad(dist_log_l._pdf, 0, 1000) out[75]: (3.47121849657489, 8.412130378805368e-10)

this break class's implementation of inverse transform sampling. generate samples domain integral of pdf 0 x first reaches 1.0, in case 2.325

in [81]: quad(dist_log_l._pdf, 0, 2.325) out[81]: (1.0000875374350238, 1.1103202107010366e-14)

that is, in fact, see in histogram.

as quick fix verify issue, modified return statement of _pdf() method to:

        return d/3.47121849657489

and ran script again. (in real fix, value function of other parameters.) commands

in [85]: import matplotlib.pyplot plt  in [86]: plt.hist(distro, bins=31)

generates plot:

plot


Comments

Post a Comment

Popular posts from this blog

node.js - Node js - Trying to send POST request, but it is not loading javascript content -

i have been trying send post request website, , has not been loading full site. i guessing problem node js not loading javascript content, executing it. can see javascript in response, though never loads content javascript files producing in html. what mean is, doesn't execute javascript. how make node js code overcome this, , wait the full website load? have tried native code, , "request' module, both producing same errors. if helps, don't need native javascript. modules fine. some code have tried (request module): var options = { method: 'post', uri: 'https://url', formdata: { 'email': 'email', 'prize': '0', 'transactional': 'on' }, headers: { /* 'content-type': 'application/x-www-form-urlencoded' */ // set automatically } }; rp(options) .then(function (body) { console.log(body) }) .catch(function (err) { console.log(err) }); when fetch content...
Read more

javascript - Replicate keyboard event with html button -

i have tried few ways make happen. have javascript pinball game uses keyboard keys controls. converting application touch screen display. workaround, hoping overlay buttons when clicked simulate keyboard strokes. have done research , sounds should work. using jquery v3.2.1 here things have tried far... html element: <input type="button" class="coil"></input> $('.coil').trigger({type: 'keydown', which: 40, keycode: 40}); with this, not errors, nothing happens. var coilkey = $('body').keydown(function(e) { switch (e.keycode) { case 40: break;} }) $('.coil').click(coilkey); this 1 returns error in console... ((jquery.event.special[handleobj.origtype] || (intermediate value)).handle || handleobj.handler).apply not function below javascript game engine handles key listeners... addkeylistener: function (keyandlistener) { this.keylisteners.push(keyandlistener); }, // gi...
Read more

javascript - Web audio api 5.1 surround example not working in firefox -

i've been playing lott lately web audio api on both firefox , chrome. few days ago started experiment surround set. when trying surround audio in web audio api came notice example works fine in chrome v59 not in firefox v54. // create web audio api context var audioctx = new (window.audiocontext || window.webkitaudiocontext)(); audioctx.destination.channelinterpretation = 'discrete'; audioctx.destination.channelcountmode = 'explicit'; audioctx.destination.channelcount = 6; var oscillators = []; var merger = audioctx.createchannelmerger(6); console.log(audioctx.destination, merger); //merger.channelinterpretation = 'discrete'; //merger.channelcountmode = 'explicit'; //merger.channelcount = 6; var addoscilator = function(channel, frequency) { var oscillator = audioctx.createoscillator(); oscillator.frequency.value = frequency; // value in hertz oscillator.connect(merger,0,channel); oscillator.start(); oscillators.push(o...
Read more