Questions tagged [probability-or-statistics]

Questions about systematic data collection and organization, or the application of probability theory to model the inherent patterns and properties of sampled data, underlying data distribution(s) or random processes.

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20 views

Using a matrix as input in KarhunenLoeveDecomposition

I have a matrix which contains realizations of a random variable. I want to perform the Karhunen-Loève decomposition over it. I also have a Matlab code with KL implemented. I have tried to do it as <...
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0answers
20 views

PredictionLimits not working for time series

I'm doing an ARIMA forecast with daily data (but that is formatted as year-month-day-hour-minute-second, although hour, minute, and second are always zero) and I'm trying to get the prediction ...
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0answers
50 views

Stochastic noise with known propability density function

How can I generate samples for random function, which functional "probability density" is known? When I say "probability density" for random function $\xi(\mathbf{q},t)$, I mean, ...
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71 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: ...
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6answers
217 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]] ...
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1answer
50 views

Unknown statistical function - groupings of permutations

Please bear with the vagueness of this question's title, as my question itself has to deal with the fact that I don't know what to call the operation I'm looking for. I have a statistical operation ...
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0answers
57 views

Adding a new statisitical distribution

What would I need to define to add a new statistical distribution to Mathematica? Ideally, it would support as many of Mathematica's statistical functions as possible. In practice, this might most ...
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1answer
41 views

Nominal variables in LinearModelFit must be specified before continuous variables

I am applying the LinearModelFit to a 90 x 5 matrix, in which the 4th variable is a nominal variable (i.e., x4 is a categorical ...
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0answers
33 views

How to calculate smoothing constant alpha in ExponentialMovingAverage?

I'm trying to use ExponentialMovingAverage on a time series, but I'm not sure how I'm supposed to calculate the smoothing constant. I read that the appropriate ...
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1answer
33 views

Simulating jump Markov process

I am trying to simulate a jump Markov process as follows. I define the process $N_j = N_{j-1} + 1$ with probability 1/2 or $N_j = N_{j-1} - 1$ with probability $1/2,$ with $N_j = 0$ as an absorbing ...
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0answers
39 views

Calculating correlational dimension using Mathematica

I am modelling such a system: $T:(x,y)\rightarrow (d+C_2(x\cos\tau - y\sin\tau),C_2(x\sin\tau+y\cos\tau))$, $\tau = C_1-C_3/(1+x^2+y^2), C_1=0.4, C_2=0.9,C_3=0.6,d=0.6$. I am applying $T$ to point $(...
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1answer
59 views

Sketching a PDF function (discrete)

I have this distribution: $Probability = 2/(cosech⁡(x))(k x^{2k}))/((2k))$ for $k$ = 1 to infinity. How can I do a sketch for any value of $x$?
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1answer
66 views

Binary (binomial) logistic regression with multiple independent variables: calculating the confidence range or prediction

Adding on top to this post here, I am looking for the confidence range (intreval) of the prediction of a multi variant binary logistic regression. Can someone extend the solution in the post ...
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51 views

Unexpected PDF in `FirstPassageTimeDistribution`

I am new to Markov Processes, and while learning the discrete Markov chain with the following matrix $$P=\begin{bmatrix}\frac{1}{3} & \frac{2}{3} & 0 & 0 \\ \frac{1}{2} & \frac{1}{2} &...
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0answers
31 views

A natural work with Missing values

For statistical procedures, is there some simple setting to automatically skip the Missing values? (e.g. Options -> "SkipMissing") The naive ...
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1answer
42 views

Does TTest taking into account the Welch's t-test?

TTest has an option VerifyTestAssumptions for "EqualVariance", does it automatically switch to Welch's t-test when variance of the two data sample differ a lot?
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1answer
95 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 ...
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0answers
32 views

Applying Cox modification to Conf. Interv. to $E(y)$ when we only observe $\log(y)$

I'm trying to apply the Cox method described in this article: Using the notation in it, let $X\sim \log N(\mu,\sigma^2)$, i.e. $Y=\log(X) \sim N(\mu,\sigma^2)$. Hence, $E(X)=E(e^Y)=e^{\mu+\sigma^2/2}$....
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0answers
292 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 ...
2
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1answer
206 views

Is it possible to ask Mathematica to give a table of probability that $f(x)>0$?

I have a function $$f(x)=(4 \cos 2 a x+3) (\cos a x+2 \cos 300 x),$$ and I want to calculate the probability that $f(x)>0$ for $a=\{1,2,3,...,100\}$ assuming that $x$ has uniform distribution. More ...
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1answer
71 views

Correlation test for $x$ and $y$ values of a list

If I have the following data: ...
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2answers
104 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: ...
3
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2answers
323 views

How to get x value where area under curve is some number?

My goal is to get x value where area under the curve (from the x ~ infinity) is about 0.05. But the code which I have tried shows errors. How to correct it? ...
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2answers
31 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 ...
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0answers
49 views

generate statistical table to complete and then review,How can I generate this exact table?

Good morning everyone I want to generate a data table model with intervals (between 5 and 15) following Sturges rule I want to generate a data table model with intervals (between 5 and 15) following ...
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1answer
41 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: ...
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1answer
50 views

Conditional Probability of first and second letters in a data set of strings

I have a dataset of strings and I would like to take only the first two letters of each string and find the conditional probability P(Second Letter|First Letter) while only looking at the words of the ...
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1answer
335 views

Need help to convert a Matlab script into a Mathematica script?

I would like to convert a small script but a little technical in Mathematica language. Here is the Matlab script : ...
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2answers
65 views

(rolling) n-weekly average

I have the data of the SPX index weekly ...
0
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1answer
31 views

Evaluating $T(x,y) = ((K_h*K_g - K_g)*(K_h*K_g - K_g))(x-y)$?

Define $K_h$ as$$ K_h(x) = \dfrac{1}{h}K\bigg(\dfrac{x}{h}\bigg), $$ where $K$ is the Gaussian function$$ K(x) = \frac{1}{\sqrt{2\pi}}e^{-\frac{1}{2}x^2}. $$ Define the function $T(x,y)$ by$$ T(x,y) = ...
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1answer
51 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 ...
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1answer
27 views

Visualize the optimal point for distribution with three parameters

I want to visualize to any distribution with two or three parameter ...
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1answer
93 views

Exponential Decay fit and printed parameters with integer data [closed]

Problem: I'm trying to plot an exponential decay curve on a set of integer data, and print the various parameters and their uncertainties on the plot itself. Having adapted code from another question, ...
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2answers
62 views

Sampling inhomogeneous spatial point processes

I am looking to generate a point process (random set of points) in a disk of radius $R$, but where the intensity measure decays, for $r$ the distance from the origin of the disk, as $\exp(-r^2/2)$. Is ...
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1answer
65 views

Getting pdf of X^2

My goal is to get pdf of x^2 with x follows N(0,1). I have tried as below but the result(at Out[41] is not what I expected(Sqrt[y] term supposed to be at denominator). How to correct? (I have Copied ...
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0answers
65 views

How does NonlinearModelFit work? [closed]

Suppose I have a model $ f (x) $ with some free parameters $ a, b $ and I want to fit my model to a data set called Dx. How does NonlinearModelFit find the value of ...
2
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1answer
65 views

Understanding the Correlation[] function in Mathematica

I have this data for four quantities measured in different temperatures: ...
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0answers
44 views

How to compute an indefinite integral for a general parameter choice?

I am trying to compute the integral: Integrate[E^(a*InverseCDF[NormalDistribution[0, 1], (1 - x)]), x] for a >= 0. The ...
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2answers
72 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 ...
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1answer
73 views

Probability of a point randomly chosen in a circle is nearest to the center [closed]

I've been having some trouble thinking about this problem for a couple days, but everything I've done has been useless, can you guys help me? Inside of a circle of radius A>0, N points are chosen ...
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0answers
24 views

LogitModelFit for predicting Categorical Variable

I was wondering how can I use LogitModelFit to predict the probability of a categorical variable based on non-categorially variables ?
2
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1answer
32 views

How to use one-way ANOVA for three groups?

I want to reproduce the Example illustrated here using Mathematica 12.0. In this example one-way analysis is applied to the following three groups of values: ...
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1answer
33 views

How to find the expected value of a parametric function?

Suppose $a \ge 0$ is a parameter and $X_1$ is an uniform random variable in $[1,4]$ and $X_2$ is an uniform random variable in $[1/2,1]$. How to find the expected value of $\max\{5-X_1a, 3-X_2a,0\}$?
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0answers
20 views

Binned Log-Maximum Likelihood

I have a dataset describing, say, radioactive decays. I studied the binned maximum likelihood method for estimating the mean lifetime. Since I am new to Mathematica, I am trying to understand how to ...
2
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1answer
111 views

Finding Chi^2 of a Non-Linear Fit Model

Question: I have some data, with a y=Ae^(-kt) model applied (It's a radioactive decay), thanks to answers on another question, the model is applied and returns the ...
2
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3answers
112 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 ...
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1answer
70 views

Why does FindDistributionParameters[] fail to converge for this distribution? [closed]

During testing my code for calculate parameters The following exception is thrown: ...
2
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1answer
58 views

'FindFit' ignoring certain data points to optimise r^2 value

As shown in the code below, ...

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