probability-density

I want to plot some points with the rbf function like here to get the density distribution of the points: if i run the following code, it works fine: from scipy.interpolate.rbf import Rbf # radial basis functions import cv2 import matplotlib.pyplot as plt import numpy as np # import data x = [1, 1, 2 ,3, 2, 7, 8, 6, 6, 7, 6.5, 7.5, 9, 8, 9, 8.5] y = [0, 2, 5, 6, 1, 2, 9, 2, 3, 3, 2.5, 2, 8, 8, 9, 8.5] d = np.ones(len(x)) print(d) ti = np.linspace(-1,10) xx, yy = np.meshgrid(ti, ti) rbf = Rbf(x, y, d, function='gaussian') jet = cm = plt.get_cmap('jet') zz = rbf(xx, yy) plt.pcolor(xx, yy, zz,

I have a multivariate probability density function P(x,y,z), and I want to sample from it. Normally, I would use numpy.random.choice() for this sort of task, but this function only works for 1-dimensional probability densities. Is there an equivalent function for multivariate pdfs? There a few different paths one can follow here. (1) If P(x,y,z) factors as P(x,y,z) = P(x) P(y) P(z) (i.e., x, y, and z are independent) then you can sample each one separately. (2) If P(x,y,z) has a more general factorization, you can reduce the number of variables that need to be sampled to whatever's conditional

I am trying to generate a plot for Lognormal Probability Density in R, with 3 different means log and standards deviation log. I have tried the following, but my graph is so ugly and does not look good at all. x<- seq(0,10,length = 100) a <- dlnorm(x, meanlog = 0, sdlog = 1, log = FALSE) b <- dlnorm(x, meanlog = 0, sdlog = 1.5, log = FALSE) g <- dlnorm(x, meanlog = 1.5, sdlog = 0.2, log = FALSE) plot(x,a, lty=5, col="blue", lwd=3) lines(x,b, lty=2, col = "red") lines(x,g, lty=4, col = "green") I even was trying to add legend on the right top for each mean log and standard deviation log, but it

I'm trying to generate random samples from a lognormal distribution in Python, the application is for simulating network traffic. I'd like to generate samples such that: The modal sample result is 320 (~10^2.5) 80% of the samples lie within the range 100 to 1000 (10^2 to 10^3) My strategy is to use the inverse CDF (or Smirnov transform I believe): Use the PDF for a normal distribution centred around 2.5 to calculate the PDF for 10^x where x ~ N(2.5,sigma). Calculate the CDF for the above distribution. Generate random uniform data along the interval 0 to 1. Use the inverse CDF to transform the

I have many points inside a square. I want to partition the square in many small rectangles and check how many points fall in each rectangle, i.e. I want to compute the joint probability distribution of the points. I am reporting a couple of common sense approaches, using loops and not very efficient: % Data N = 1e5; % number of points xy = rand(N, 2); % coordinates of points xy(randi(2*N, 100, 1)) = 0; % add some points on one side xy(randi(2*N, 100, 1)) = 1; % add some points on the other side xy(randi(N, 100, 1), :) = 0; % add some points on one corner xy(randi(N, 100, 1), :) = 1; % add

I want to convert fitted distribution to frequency. import numpy as np import matplotlib.pyplot as plt from scipy import stats %matplotlib notebook # sample data generation np.random.seed(42) data = sorted(stats.lognorm.rvs(s=0.5, loc=1, scale=1000, size=1000)) # fit lognormal distribution shape, loc, scale = stats.lognorm.fit(data, loc=0) pdf_lognorm = stats.lognorm.pdf(data, shape, loc, scale) fig, ax = plt.subplots(figsize=(8, 4)) ax.hist(data, bins='auto', density=True) ax.plot(data, pdf_lognorm) ax.set_ylabel('probability') ax.set_title('Linear Scale') The above code snippet will generate

I have a set of >2000 numbers, gathered from measurement. I want to sample from this data set, ~10 times in each test, while preserving probability distribution overall, and in each test (to extent approximately possible). For example, in each test, I want some small value, some middle class value, some big value, with the mean and variance approximately close to the original distribution. Combining all the tests, I also want the total mean and variance of all the samples, approximately close to the original distribution. As my dataset is a long-tail probability distribution , the amount of