All Questions
Tagged with distributions probability-or-statistics
544 questions
4
votes
2
answers
499
views
Polynomial fitting to obtain the growth rate
We -- my friend -- had asked a question here, which was not completely related to Mathematica, however, in a hope that someone familiar with the topic could help. There are still some aspects which we ...
user82988
1
vote
2
answers
173
views
How to obtain the variance of a chi-squared distribution with Mathematica
I'm new to Mathematica and would like to show that for $x_1, ..., x_k$ independent, standard normal random variables the variance of the sum of their squares, i.e., $var(\sum_{i=1}^kx_k^2)$, is equal ...
- 13
1
vote
2
answers
48
views
`KernelMixtureDistribution` error message about precision
I want to use KernelMixtureDistribution to deal with a large amount of data points. For example, the following codes shows how I use it:
...
- 2,295
2
votes
1
answer
204
views
Finding distribution of sum of two dependent variables
I am trying to find the distribution of the sum of two random variables $(x_1,x_2)$ which have the following distribution:
$$f(x_1,x_2) = \begin{cases}2 ( x_1 + x_2) & 0 \le x_1 \le x_2 \le 1 \\ 0 ...
- 51
7
votes
1
answer
127
views
How to calculate a PDF of a neural network output?
I have to find the probability density function of the output of an internal layer in a neural network.
I wanted to do it using NetMeasurements adding a layer like
<...
- 215
5
votes
1
answer
175
views
What is the default binning method of Histogram[]?
Histogram[] command returns a histogram of a set of data. There are different methods of binning, such as, Scott's rule, which we can specify the binning method in Mathematica. My question is what is ...
- 65
1
vote
1
answer
379
views
2D kernel density estimation (SmoothKernelDistribution) with bandwidth estimation: what are the values that Mathematica chooses?
Mathematica has built in bandwidth estimation including the rules Scott, SheatherJones and ...
- 671
1
vote
2
answers
211
views
2
votes
1
answer
61
views
Are there any issues/best practices/suggestions when working with a DataDistribution instead of a distribution?
Suppose there is a random variable $X$ that can take on values $-1,0,1$, with probabilities $P(X=1)=P(X=-1)=.25$ and $P(X=0)=.5$.
How can I work with such a random variable in mathematica? (Find the ...
- 829
0
votes
0
answers
49
views
I have found out CDFs of 2 data and listed them. I need to find out the composition of such 2 CDFs
x= RandomVariate[ExponentialDistribution[2], 10]
y = RandomVariate[ExponentialDistribution[3], 10]
f = EmpiricalDistribution[x]
...
1
vote
2
answers
301
views
Any suggestions for improving my fitting?
This is not a completely Mathematica question, but I hope people who are familiar both with Mathematica and statistics could help me on this.
I have a set of data as
...
1
vote
1
answer
108
views
Proper probability distribution formatting for DistributionFitTest
I am trying to use an exponentially modified gaussian to fit a distribution, but I think I may be misunderstanding something about how probability distributions work in Mathematica.
Running
...
- 21
11
votes
1
answer
490
views
Can LearnDistribution learn conditionality?
I would like to apply LearnDistribution to multivariate conditional distributions. Here's a simple artificial example:
...
- 31.8k
1
vote
0
answers
62
views
Implementing approximatePDF function
Sometimes distribution is too complicated for built-in PDF command, so it would be useful to have approximatePDF[dist,x,n] which ...
- 6,697
5
votes
2
answers
334
views
Transformation of random variable
I am looking to recreate a derivation of a PDF using a transform of random variables. I did the original derivation in Mathematica with the Mathstatica package, but when I updated Mathematica recently ...
- 609
1
vote
1
answer
83
views
Ratio involving CDF and PDF of a standard normal random variable behaves unexpected when plotted
Good morning,
I am plotting the function $h[x]$, see below, and obtain an oscillating behavior in the range $x \in [7.2,8.3]$ that cannot be explained by the function itself. Also for $x \ge 8.4$ it ...
- 11
4
votes
1
answer
512
views
How to make a bar graph like this?
I've read some article recently and because I've been doing the same calculations so far, I wanted to have a graph like this:
by the looks of it, it certainly looks like it was done in mathematica, ...
1
vote
1
answer
125
views
Sample discrete distributions with a good range of observed entropies
For a numerical sanity check, I need to sample random sequences of $n$ positive numbers adding up to 1, and having a high chance of observing both high entropy and low entropy sequences. Compute the ...
- 6,697
3
votes
1
answer
194
views
How to generate random variate in custom domain for a distribution?
I have a distribution defined in a particular domain of the variable but now I want to generate a random variable not in the entire domain but only in a subset of the domain. Here is what I'm trying ...
user51833
0
votes
0
answers
78
views
How to find the appropriate fit?
Imagine we are given this set of data:
data = {{0, 1}, {1, 0}, {3, 2}, {5, 4}, {6, 4}, {7, 5}};
We fit the data with:
...
user80433
-1
votes
1
answer
132
views
Compute the likelihood from pdf : $L= \prod^{n}_{i} p(x_{i})$
I would like to use the product value in order to derive the likelihood. Say we have a Gaussian pdf $p(x_{i})$ for $\{i\}_{i=1}^{n}$ and define the likelihood as $L= \prod^{n}_{i} p(x_{i})$.
Example 1:...
- 109
4
votes
6
answers
298
views
How can we use TransformedDistribution to infer the sampling distribution of the sample mean?
As we know, TransformedDistribution can infer a distribution of a transformation like
TransformedDistribution[A*X + B, X \[Distributed] NormalDistribution[μ, σ]]
...
- 27.2k
0
votes
1
answer
338
views
Sketching a PDF function (discrete)
I have this distribution: $Probability = 2/(\operatorname{cosech}(x))(k x^{2k}))/((2k))$ for $k$ = 1 to infinity.
How can I do a sketch for any value of $x$?
1
vote
1
answer
162
views
PDF of sum of (1/(1+uniform distribution)) and a normal distribution
I have a continuous uniform random variable $P∼U(0,1)$ and a normal random variable $X∼N(0,σ)$. If $Z$ is given by $Z=\frac{1}{1+P}+X$ where $X$ and $P$ are independent variables, how can I calculate ...
- 11
5
votes
0
answers
403
views
Histogram (automatic binning)
There are different methods for choosing widths of bins for a histogram, like Freedman-Diaconis rule. In Mathematica, without choosing a specific method, with the command ...
user79703
2
votes
2
answers
131
views
Mathematica can't seem to handle Truncated BinormalDistribution when there is non-zero correlation coefficient
I would like to use Mathematica to analyze (e.g., compute moments, plot, etc) a truncated bivariate normal distribution. For example:
...
- 29
0
votes
2
answers
124
views
Normalize an L(s, d) function for fixed s
I have the following function L:
σ = 9;
L[s_, d_] = (1/(σ*Sqrt[2*\[Pi]]))*E^(-(1/2)*((s-(-50-11*Log[d]))/σ)^2)
This function L describes basically for some ...
- 291
2
votes
1
answer
335
views
CDF function from list
How can I get the CDF for a list of values containing the value of a random variable and its probability?
I have:
...
2
votes
1
answer
76
views
How to find sum of squares of data from a multivariate (Dirichlet) distribution? [closed]
Let $X = Dirichlet(1,1,1)$ be a tri-variate random variable with Dirichlet distribution with parameters all equal to 1. I need to find what $X_1^2+X_2^2+X_3^2$ will be.
I did ...
- 21
5
votes
1
answer
128
views
Mean of TransformedDistribution returns wrong result
I want to compute the mean of this transformed distribution $10^{(25+5x+y)/5}$, where $x$ and $y$ are independent normal random variables.
Here is my code
...
- 51
1
vote
2
answers
130
views
TransformedDistribution not returning a function
I'm trying to use TransformedDistribution to find the distribution of a function of two variables that have Normal distributions.
The function is $h(x, y)=x^2+y^2$.
I tried to do this two ways, first ...
- 37
2
votes
3
answers
206
views
Chen weibull distribution
I write the density function of cw distribution and add data to calculate parameters maximum likelihood but the results of Mathematica no like the research
...
- 59
6
votes
2
answers
253
views
Why is the conditional probability not working for `CategoricalDistribution`?
Bug introduced in 12.1 and fixed in 12.3
Consider the following simple example for demonstration:
...
- 9,751
2
votes
1
answer
415
views
Entropy of a distribution
I need to calculate the entropy of a distribution from raw data. I found two approaches here and here.
But it seems they don't work for my case.
My data is:
...
user77316
1
vote
1
answer
265
views
0
votes
1
answer
93
views
Skewness and central moment
I have distribution which I want to calculate the third order moment function of my distribution. I got confused what is different between Moment third order and ...
- 3
1
vote
0
answers
63
views
Create CDF from a custom function
I have a complex function as follows (sorry for ugly script due to many parameters in the code!) which gives CDF of some data. I wonder whether there's any way to write it in CDF form in Mathematica, ...
- 11
2
votes
2
answers
246
views
0
votes
0
answers
117
views
How to go from a Pareto Distribution in Scipy to a Pareto Distribution in Mathematica?
Assume that I have fitted a Pareto distribution via Scipy and have gotten the following parameters:
...
- 1
0
votes
1
answer
112
views
Evaluation points following a bivariate Gaussian distribution [closed]
I have a function of two variables, say $f(a, b)$, which I want to evaluate (and later average) in the neighborhood of $a=0$ and $b=0$, with density of points around $(a,\,b)$ following a Gaussian ...
- 1,225
1
vote
2
answers
120
views
Expectation with conditional random variable [closed]
Given an Exponentially Distributed Random Variable $X\sim \exp(1)$, I need to find $\mathbb{E}[P_v]$ in Mathematica, where $P_v$ is given as:
...
- 113
2
votes
2
answers
167
views
3
votes
2
answers
280
views
Estimation of the expected Euclidean distance between two random points on a unit $n$-hemisphere
What is the best approach to estimate, with Wolfram Mathematica, the expected Euclidean distance (in a $(n+1)$-dimensional space) between two points selected uniformly at random on a unit $n$-...
1
vote
1
answer
376
views
How to find the inverse of CDF of geometric function? [closed]
The cdf of geometric distribution is given by $ F(x)=1-(1-p)^x$.
I want to calculate the inverse of it, for example, $F^{-1}(U)$
I am doing the following
...
- 565
2
votes
3
answers
523
views
Estimate the expected distance between two random points on the unit $n$-sphere [duplicate]
What is the best approach to estimate, with Wolfram Mathematica, the expected Euclidean distance in a $(n+1)$-dimensional space between two points selected uniformly at random on the unit $n$-sphere? ...
2
votes
1
answer
270
views
Raising the normal distribution curve to a specified height on the $y$-axis
I'd like to know how to fit the normal distribution curve between $x$ and $y$ values so that the curve maintains its bell shape. I guessed the sigma is the scale ratio, but it doesn't work as I ...
- 123
3
votes
1
answer
87
views
Failure in MultinormalDistribution
My RandomVariate fails to evaluate when sampling from a multinormal distribution, any idea what's happening here?
This is Mathematica 12.1 on Mac:
...
- 6,697
1
vote
0
answers
41
views
Speed up exact distribution of the sum of the top $k$ statistics on a bounded discrete uniform distribution?
I came across a nice answer by Sasha (I believe a Wolfram engineer) on mathematics stack exchange regarding the distribution of the sum of the top $k$ order statistics. (This was an answer to an RPG ...
- 26k
2
votes
1
answer
136
views
Intepreting the results of DistributionFitTest, and other alternatives in Mathematica 12.1
I have been playing with DistributionFitTest as a means of testing how normal some data sets I have. I've been working with some simulated data sets so I can try ...
- 2,530
0
votes
2
answers
566
views
How to plot this pdf?
Let $x\sim N(\mu,\sigma^2)$ and $y=\max\{e^{x-1}-\kappa,0\}$. How to get and plot the pdf of y? In particular, there will be a probability mass at $y=0$, which is a nondifferentiable point. I tried
<...
- 213