Questions tagged [distributions]
For questions about distributions built-in in Mathematica, and functions that operate on them. Also includes questions about defining your own distributions.
820
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Is there any general solution exist for $\sum_{i=1}^{N} \frac{1}{B(x+i, i)}$ function? [closed]
$\sum_{i=1}^{N} \frac{1}{B(x+i, i)} = \frac{1}{B(x+1, 1)} + \frac{1}{B(x+2, 2)} + \ldots + \frac{1}{B(x+N, N)}$
where ${N}$ is fixed value. is there any simple expression exist for x in the above ...
- 43
0
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2
answers
57
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Modifying horizontal axis of a PDF plot
I have a bunch of particles that I can measure their volume.
PDFs of the size distribution by volume of particles, v(a), measured are reasonably well represented by lognormal distributions of the ...
- 337
3
votes
0
answers
62
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How can I calculate P-Value for a custom distribution?
I used DistributionFitTest but it works only with a defined distribution.
This is the distribution that I used:
...
- 59
4
votes
3
answers
214
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Integration involving two DiracDelta with variable limit
I want to write a code to evaluate
$$ \int_0^{t-1}\frac{\delta(z-1)}{z}\frac{\delta(t-z-1)}{t-z}dz$$
which should gives the answer $$\frac{\delta(t-2)}{t-1}.$$
I tried to write the code
...
- 179
2
votes
1
answer
92
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SIR Parameter Estimation in Mathematica
All infected individuals go through an incubation period, which lasts on average for 4 days. During this time, individuals are not infectious, nor do they have any excess mortality risk.
All infected ...
2
votes
1
answer
118
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Convert R code to Mathematica code of Poisson log-likelihood for the epidemic curve
I want to define a function that simulates the model for a given combination of parameters and calculates the Poisson log-likelihood for the epidemic curve of reported cases:
...
0
votes
1
answer
36
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Trying to use ProbabilityDistribution for custom distribution - Getting errors/warnings I don't understand
I have this custom distribution that I want to use in Mathematica, but there
appears to be some sort of problem I don't understand.
Also, when I compute the mean for the custom distribution via
...
- 427
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0
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39
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Combinations of distributions to be called with `RandomVariate`
I'd like to manipulate distributions that I'm going to retrieve using RandomVariate; e.g., I would like to take
...
- 153
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1
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96
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Unable to check own distribution
Good afternoon I need to estimate different distributions from some data. Among these distributions, it is necessary to use the Kritsky-Menkel distribution. I set a formula for the distribution ...
- 1
2
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2
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118
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Calculating Distributions that Have Dependencies
I want to calculate a distribution from a function that depends on several variables, where there is an interdependency between the variables. This works:
...
- 133
2
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1
answer
72
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What distribution corresponds to the asymmetric Around?
The documentation for Around, https://reference.wolfram.com/language/ref/Around.html, indicates that
For linear computations, Around[x,δ] behaves like a number whose values are distributed according ...
- 210
1
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2
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120
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What is the best (fastest and accurate) way to obtain PDF from the given dataset?
Consider some list of two coordinates, points, generated by some arbitrary function function1 (which is a pdf up to a ...
- 4,984
1
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3
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181
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How to extract as large a number as possible by random sample? [closed]
When I extract a element from a list by random sample, I want to extract as large a number as possible
(It mean it's not always extracted the max value.)
For example, when I take a element by random ...
- 220
0
votes
1
answer
36
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Expression for variance of a truncated distribution as a function of the point of truncation
I am working on a project where I need to calculate variance of a truncated distribution. Suppose $X$ has some distribution and $x\in\mathbb{R}$. I am interested in $var(X|X\leq x)$. Given some ...
- 143
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1
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58
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How is InverseErf related to the inverse normal distribution?
The inverse function of the standard normal cdf is
f[x_] := InverseCDF[NormalDistribution[0, 1], x]
I also have
...
- 259
2
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0
answers
62
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Mathematica unable to realize simple distributional relationship
I was trying to find the CDF for the following problem:
...
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3
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3
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251
views
0
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1
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78
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Expansion of standard inverse normal cdf
Let $\Phi: x\rightarrow y$ be the CDF of a standard normal distribution. The range of $\Phi(x)$ is $[0,1]$ and the domain is all real numbers.
I want to get a series expansion of $\Phi^{-1}(y)$ around ...
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0
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59
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I am unable to improve the (MAProcess) time series model
I am a time series novice and have been learning the art/trade from examples while being governed by the NIST handbook (ch.6, sec.4).
My question is regarding:
How to improve the estimated time ...
- 5,311
0
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0
answers
21
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Creating Process Template from FindDistribution
may i ask if anybody knew where i wrong please? Im stuck in this step.
I want to visualize Hidden Markov Model in which state from 2-20 is best with continuous emission, but it need starting value ...
-1
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1
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113
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0
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1
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108
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3
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2
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80
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Why does Maximize return this unevaluated?
Maximize[{PDF[NormalDistribution[0, sigma], x], sigma > 0}, x, Reals]
Just returns unevaluated (when, obviously, it should return ...
- 3,167
1
vote
2
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148
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Probability of a point being from the same distribution as sample [closed]
I have a sample of two-dimensional points {{x_,y_1},..{x_n,y_n}}, I've built a linear regression line, there seems to be a correlation between X and Y (Pearson's 0.662 if that matters).
Now what I ...
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1
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66
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Conditional Expectation of an autoregressive (AR1) Process
Suppose X is a time series that follows the process:
$X[t]=\rho X[t-1] + \varepsilon[t]$
where $\varepsilon[t] \sim \mathcal{N}(0.0, \sigma)$, $\varepsilon[t]$ is IID and $X[0] \sim \mathcal{N}(0.0, \...
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3
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345
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Finding the mean and variance of a distribution
I have tried unsuccessfully to use Mathematica to derive both the expected value (mean) and variance of a particular statistical distribution of interest to me.
The distribution is a discretized ...
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1
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2
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103
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How to sample from a `MultinormalDistribution` with a positive semidefinite covariance matrix?
I'm trying to sample from a Gaussian process (GP) following these tutorials:
https://peterroelants.github.io/posts/gaussian-process-tutorial/#Sampling-from-prior
https://stephens999.github.io/...
- 155
1
vote
0
answers
36
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Plotting a parametric function for a given prior distribution of parmaeters
I have a function $f(x, \alpha, \beta)$. The function is piecewise defined and not analytically integrable. I would like to do the following: draw from a distribution on $\alpha$ and $\beta$, compute $...
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3
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497
views
How to plot the the maximum likelihood estimates?
I would like to find the code for the graphical representation of the maximum likelihood estimates. For that first, I find the estimate values using the the code given below
...
- 159
0
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0
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46
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How does Mathematica work with multivariate distributions?
I recently found the AEP algorithm. Curious how Mathematica would handle the situation, I made an experiment:
...
- 123
0
votes
1
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71
views
How to obtain smooth distribution for the given datasets?
Consider a variable x defined in the range
$$
\tag 1 x \in (1,10^{7})
$$
Let us assume that we have three datasets belonging to three different intervals of x:
...
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2
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How to plot correct empirical distribution?
I have data that represents number of values in intervals.
So, I have intervals like: [0,1], [1,2], [2,3] and so on.
My data is [23,11,3], which means in interval [0,1] there are 23 values, inside [1,...
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Modeling Experimental data with a CDF
I have some data plotted above which relates two variables that were derived experimentally. I'm trying to fit a cumulative distribution function to it so that we can take a sample of Y at X. I've ...
- 1,156
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0
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71
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Discrete Plot of a complicated function containing Dirac delta or discrete delta function
I have tried to obtain the discrete plot of the following distribution function, which contains summations and integrations along with Dirac delta function, the Mathematica code of which is given ...
0
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0
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31
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Slow SmoothKernelDistribution of WeightedData
Consider some data in the form
data = {{x,y,weight(x,y)},...};
I make
wd = WeightedData[data[[All,{1,2}]],data[[All,3]]];
I ...
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Parameter distribution from NonlinearModelFit result
Is it possible to construct a parameter distribution (e.g. Normal or StudentT) from the Estimate and Standard Error of a NonlinearModelFit result? The SE is the square root of the variance but what is ...
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1
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1
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63
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How can I calculate the moments of a truncated random variable?
I am using the Moment function to calculate the moments of an exponential random variable.
as follows,
Moment[ExponentialDistribution[3], 9]
However, I need to ...
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4
votes
1
answer
66
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Speeding up RandomVariate with custom probability distribution
I have the defined a custom distribution, which is a Gaussian where the exponent can be any real n greater than 0 (set to actually be >0.5 in use), i.e.
...
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1
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How to generate random value under the given distribution fast?
Consider a distribution
distr[EN_, Enu_, mN_] =
Exp[-(Sqrt[EN^2 + mN^2]/Enu)]*Sqrt[(Sqrt[Enu^2-mN^2]/2)^2 - EN^2] Sqrt[
EN^4 - (Enu/4)^4]
where mN is a free ...
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124
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0
votes
1
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84
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I have a problem in log likelihood which I wrote for custom distribution
I have a custom distribution and data as follows
...
- 359
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0
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21
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Estimate parameters from random samples drawn from a copula distribution [duplicate]
I defined a copula distribution as follows:
...
- 359
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1
answer
72
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what is wrong in my code for calculate parameters bivariate distribution?
data is i,j as x, y as in pic
...
- 359
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votes
1
answer
101
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How to find maximum likelihood parameter estimates for a custom bivariate distribution?
this is univariate distribution
...
- 359
1
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3
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82
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How to restrict FindDistribution to real-valued distributions
The following seems buggy to me, but perhaps I'm confused about something. Or maybe there's a workaround that makes it moot?
First, I ask Mathematica to find a distribution that describes a dataset ...
- 606
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1
answer
98
views
How to write a Bivariate custom distribution, calculate p value and other properties?
This distribution is univariate
...
- 359
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1
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How to plot copula using contourplots
I want to contour plot some copula cases for illustrative purposes in a paper. New user here, so apologies if this is straightforward. An example (taken from another source) is below of what I had in ...
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0
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how i write this custom distribution power function distribution i want to write in family distribution?
this is basic pareto distriibution
...
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1
answer
123
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Mean not working with Gamma convolution distribution
Using v 13.01 or 13.1: bug in integrate, see accepted answer below.
First off, the distribution ...
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