Questions on the statistical functions of Mathematica.

learn more… | top users | synonyms

14
votes
2answers
1k views

Obtaining joint distributions and conditional distributions using Mathematica

I have two multivariate Gaussian distributions $p(x)$ and $p(z)$ with mean vectors $m_x$ and $m_z$, and covariance matrices $\Sigma_x$ and $\Sigma_z$. my model is a simple linear model $x = W z+n$ ...
3
votes
2answers
110 views

Getting the Cumulative Distribution Function of f(x) from a dataset of x

I've a data set $\mathcal{X}$ which consists of randomly generated numbers. Let's say for example data = RandomVariate[ExponentialDistribution[1], 10^4]; My aim ...
1
vote
3answers
155 views

Plotting a frequency function

I have a list of numbers and I want to plot the fraction of numbers >= k against k which will naturally be a decreasing curve. How do I do that?
4
votes
2answers
272 views

Numerical Integration with InverseErfc

I am trying to numerically integrate an equation that involves InverseErfc (embedded in the copula defined). The equation looks like the following: $$ \int_0^T \int_0^\infty \int_0^\infty ...
0
votes
1answer
70 views

On plotting the Weibull distribution

First: How can I plot the Weibull distribution with parameters a = 2 and b = 3.5 on the range of ...
3
votes
2answers
144 views

QuantilePlot silliness

When I do a quantile plot of two large data sets (in my case, each of them of size around 3 million), the resulting notebook cell is huge, and if you save it as PDF, the resulting PDF is 13MB in size. ...
2
votes
1answer
74 views

Choosing The Best Fitted Probability Distribution Model

The following Example 20 Obs and i used Goodness of fit test with Exponential distribution, another time with Weibull distribution and third time with Pareto distribution .All of them are significant ...
1
vote
1answer
54 views

Estimating Confidence Interval Variance covariance matrix from weibull distribution

In The following Example 50 obs . I estimated distribution parameters (by point) but *i want to estimate parameters by confidence interval and calculate covariance matrix i need help * ...
2
votes
1answer
45 views

Meaning output ANOVA post hoc tests

I am carrying out an ANOVA in Mma, and I wanted to apply a post-hoc test, but I do not understand the output that is given. It says e.g. Model-> Duncan, {4, 5} ...
0
votes
1answer
63 views

Estimating Parameters of a Custom Distribution

The problem is I can not get estimation of parameters of any custom probability distribution (distributions are not built in Mathematica), here is an example: First: I entered random numbers of ...
2
votes
1answer
84 views

Probability evaluation fails with equals condition

The following evaluation fails (the result is just the copy of the input) $$\text{Probability}[0<x\leq a | x-y=t,\{x\ {ExponentialDistribution}[\lambda ],y\ {ExponentialDistribution}[\lambda ...
1
vote
1answer
115 views

Modify BinList to give elements indices in list instead of giving the list elements belonging to each bin

How could I use BinList to give elements indices in list instead of giving the list elements belonging to each bin ? Thanks.
21
votes
5answers
3k views

Showing the correlation of two variables using a plot

I have a list of $\{x_i,y_i\}$ pairs and I want to show that $x_i$'s and $y_i$'s have positive correlation. The result of ...
0
votes
0answers
25 views

Standard error of slope estimator [migrated]

Can someone please help explain this. I know the answer is a). Or provide a link with more information. The slope estimator, β1, has a smaller standard error, other things equal, if a) there is ...
0
votes
1answer
544 views

PDF of binomial distribution and mixed binomial distribution

I want to plot the PDF of binomial distributed function and a mixed binomial distributed function, therefore I entered for the binomial distribution function the following: ...
2
votes
0answers
56 views

How to include confidence intervals into ProbabilityScalePlot?

I use ProbabilityScalePlot[data, "Weibull"] to plot measured data and ...
5
votes
1answer
276 views

Estimation of vector autoregressive (VAR) process

To estimate 1-dimensional VAR process (which is AR process) you can easily use functions EstimatedProcess or ...
4
votes
1answer
151 views

Calculate the covariance of a large matrix

I have to compute the covariance of 50 very large integer matrices (2500x2000 elements). However, according to my estimation this will take around 10 days. Do you have any ideas how to speed things ...
3
votes
1answer
53 views

TransformedDistribution with respect to new variable

Given a custom pdf $f_x(x)$, I'm trying to find it's transformation $f_y(y)$ where $$y=x^2$$ and $$f_x(x)=30*x^2 (1 - x)^2, 0<x<1$$ I tried to using the following commands: ...
2
votes
0answers
45 views

k-means clustering using squared correlation in Mathematica

I am trying to cluster data using the squared correlation coefficient since in the case of my data, -1 correlation is equivalent to 1 correlation (polarities do not matter). How can this be done in ...
1
vote
1answer
113 views

Statistics confusion

I have two data sets. When I do a QuantilePlot[data1, data2], I get the graph below. However, ...
3
votes
1answer
49 views

How to use a custom CDF in a Kolmogorov-Smirnov test

How do I use a custom CDF that I defined for a Kolmogorov-Smirnov test. I have one input vector of data whose CDF I claim to have derived but want to check whether it agrees with my closed form ...
22
votes
3answers
613 views

Which Distributions can be Compiled using RandomVariate

Recently, Oleksandr kindly showed a list of Mathematica commands that can be compiled. RandomVariate was part of that list. However, whether this can be compiled depends upon the distribution that is ...
4
votes
2answers
75 views

Behavior of Commonest when there is an even split between the elements of the list it is given

How can I alter Commonest so that, when I give it an input of four zeroes and ones such as $\{0,1,1,0\}$, which has an even split in its elements, it returns the ...
1
vote
0answers
94 views

Is this the correct method in using bootstrapping to determine a lower confidence bound?

Quite often in industry, due to cost and schedule constraints, decisions must be made on small sample size data. I have 4 cycles-to-failure values resulting from running samples to failure in a ...
7
votes
3answers
528 views
1
vote
1answer
66 views

Stochastic Approximation and Simulation using Running Median

I have a function $$F(X_{t+1},Y_{t}^{med})= \alpha X_{t+1} + (1-\alpha) Y_{t}^{med},$$ where $$Y_{t}^{med} = Median(Y_1, Y_2,... Y_t).$$ Moreover, $Y_1 = X_1$ and $Y_t = F(X_{t},Y_{t-1}^{med})$ ...
5
votes
3answers
147 views

Creating Correlation Table (and Working) With Missing Data

I am working with data that contains missing values (I have several variables (across the columns) and several observations (across the rows) in an excel spreadsheet). Example of the data structure: ...
4
votes
1answer
95 views

Correlation test issues

When using Correlation[] function I sometimes get the strange warning: ...
5
votes
1answer
157 views

Simulation Sample Paths for Stochastic Approximation Algorithm

Let $X_t$ be IID random variables in $[0,1]$ and CDF $F(\cdot)$. Suppose there exists a variable $Y_t$ given by: $Y_1 = X_1$ and $Y_t = \phi(X_t, \overline{Y}_{t-1}), \forall t >1$, where ...
1
vote
0answers
36 views

Truncated Distribution Parameter Search Produces Singular Jacobian Using FindRoot

I'm trying to find the 2 parameters of a truncated Weibull distribution using version 10 and FindRoot. I would like to truncate the distribution between t =0 and t = 3600 with the probability of ...
7
votes
0answers
129 views

Median of Dataset in Mathematica 10

I'm having trouble calculating the median of a Dataset[] in Mathematica 10. The situation is as follows. Consider a dataset that was defined as follows: ...
6
votes
3answers
141 views

Expected sum of largest 3

I pick 4 numbers from the Uniform Distribution. I need the expected value of the sum of the 3 largest. I am pretty sure that the answer is 9 / 5 which agrees with a simulation. I would like to get ...
3
votes
2answers
278 views

SinglePredictionBands versus MeanPredictionBands from NonlinearModelFit

From my Statistics lectures I know the term confidence and prediction interval, whereas the confidence interval is smaller than the prediction interval. If I plot the mean and single prediction bands ...
1
vote
1answer
111 views

Simulation Beta Distribution

Suppose a function such as: $\phi^{\alpha} (x,y) = \left\{ \begin{array}{l l} \alpha x & \quad \text{if $x < y$}\\ x & \quad \text{if $x = y$}\\ \alpha x + (1 -\alpha) & ...
1
vote
2answers
212 views

build and estimate a time series process

I want to generate an EGARCH process. My problem is that I do not see how to create new processes beyond those available. The process itself is : $$\epsilon(t) = \sigma(t) \eta(t)$$ ...
0
votes
1answer
55 views

Solving minimum length confidence interval problem

I'm trying to find the minimum length of a confidence interval for the variance from a sample iid with normal distribution. I tried ...
0
votes
1answer
55 views

Can I use boolean parameters in LogitModelFit?

For example, to use 1 as True and 0 as False: ...
6
votes
4answers
232 views
2
votes
1answer
72 views

ZTest result not making sense

I'm using version 10. I'm having difficulty with understanding why I'm getting some output from the ZTest function. Here is the code for my specific example. ...
4
votes
1answer
188 views

BoxWhiskerChart - 10-90th percentile instead of min - max

I am trying to draw a custom BoxWhiskerChart with alternative values determining fences. I have data that has a lot of outliers and I have to compare it to another chart that has 10-90th percentile ...
2
votes
0answers
48 views

Why do EstimatedDistribution and DistributionFitTest work this way

I am fitting some time-series data to both a stable distribution and a normal distribution in order to assess the goodness of fit of each. Along the way I encountered the following confusing result. ...
25
votes
3answers
2k views

Histograms with pre-counted data

I've got some large data sets which have been counted but not binned already - essentially, a list of pairs of values (not bins) and counts.* (Or, equivalently, it's been binned into too-small bins.) ...
0
votes
1answer
136 views

Fitting data to a Poisson distribution

I'm trying to fit a Poisson Distribution to data produced in a lab. I've successfully made a Histogram of the data, which looks like: However, when I try to fit the Poisson Distribution using: ...
2
votes
2answers
154 views

Finding Expectation of function of a Log-normal distribution

Say $Y=g(X)$ and $p_X = \frac{e^{-\frac{(\mu -\log (x))^2}{2 \sigma ^2}}}{\sqrt{2 \pi } x \sigma }$ is Log-normal density function: [Wiki] Find E[Y]? Since $E[Y] = \int_0^\infty y f_Y \ dy = ...
0
votes
2answers
132 views

Error function fit of data

I have this experimental data set which I know should follow the Complementary error function. My goal is to find the σ of the associated gaussian distribution. However, I cannot seem to do it in ...
2
votes
2answers
159 views

Measures of association, Concordant and Discordant

I want to calculate concordant and discordant pairs on nx2 tables. ...
15
votes
2answers
331 views

Visualization: elliptical insights into data sets…

I was recently reading the following paper on visualization techniques using ellipses to gain statistical insights. Elliptical visualization for looking at correlations has briefly been touched on ...
0
votes
1answer
107 views

Generating a list of standard normal random variables

Im trying to generate a list of random (standard) independent normal variables. For this, I first generate a random list of, say, 100 real numbers in the range [0, 1000], and then make them standard ...