# 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.

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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 ...
57 views

### 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 ...
62 views

### 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: ...
214 views

### 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 ...
92 views

### 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 ...
118 views

### 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: ...
36 views

### 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 ...
39 views

### 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 ...
96 views

### 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 ...
118 views

### 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: ...
72 views

### 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 ...
1 vote
120 views

### 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 ...
1 vote
181 views

### 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 ...
36 views

### 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 ...
1 vote
58 views

### 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 ...
62 views

### Mathematica unable to realize simple distributional relationship

I was trying to find the CDF for the following problem: ...
251 views

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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 ...
1 vote
59 views

### 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 ...
21 views

### 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 ...
113 views

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### How to find Specific Fit of a Distribution?

I want to fit a data set: ...
80 views

### Why does Maximize return this unevaluated?

Maximize[{PDF[NormalDistribution[0, sigma], x], sigma > 0}, x, Reals] Just returns unevaluated (when, obviously, it should return ...
1 vote
148 views

### 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 ...
66 views

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 ...
46 views

### How does Mathematica work with multivariate distributions?

I recently found the AEP algorithm. Curious how Mathematica would handle the situation, I made an experiment: ...
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: ...
1 vote
124 views

### 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,...
1 vote
57 views

### 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 ...
71 views

### 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 ...
31 views

### 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 ...
57 views

### 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 ...
1 vote
63 views

### 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, 9] However, I need to ...
66 views

### 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. ...
81 views

### 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 ...
124 views

### I have a problem writing a custom distribution

I wrote the Frechet Distribution as follows: ...
84 views

### I have a problem in log likelihood which I wrote for custom distribution

I have a custom distribution and data as follows ...
21 views

### Estimate parameters from random samples drawn from a copula distribution [duplicate]

I defined a copula distribution as follows: ...
72 views

### what is wrong in my code for calculate parameters bivariate distribution?

data is i,j as x, y as in pic ...
101 views

### How to find maximum likelihood parameter estimates for a custom bivariate distribution?

this is univariate distribution ...
1 vote
82 views

### 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 ...
98 views

### How to write a Bivariate custom distribution, calculate p value and other properties?

This distribution is univariate ...
1 vote
113 views

### 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 ...
109 views

### What's wrong in my custom distribution?

i want to write this function ...