Questions on the statistical functions of Mathematica.

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3
votes
1answer
83 views

FindClusters Giving Wrong Groupings

I am having trouble getting FindClusters to find the right clustering for this set of data (and many other sets of data similar to it): ...
0
votes
0answers
64 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 ...
0
votes
1answer
497 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: ...
7
votes
3answers
508 views
1
vote
1answer
58 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
116 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
89 views

Correlation test issues

When using Correlation[] function I sometimes get the strange warning: ...
5
votes
1answer
137 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 ...
4
votes
2answers
253 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 ...
1
vote
0answers
24 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
112 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: ...
21
votes
3answers
549 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 ...
6
votes
3answers
138 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 ...
2
votes
2answers
239 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
86 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
201 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 : $$\epsilon(t) = \sigma(t) \eta(t)$$ ...
1
vote
1answer
95 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.
0
votes
1answer
47 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
51 views

Can I use boolean parameters in LogitModelFit?

For example, to use 1 as True and 0 as False: ...
6
votes
4answers
216 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
172 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
41 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
96 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
110 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
112 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
151 views

Measures of association, Concordant and Discordant

I want to calculate concordant and discordant pairs on nx2 tables. ...
14
votes
2answers
318 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
84 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 ...
16
votes
3answers
2k views

Standard errors for maximum likelihood estimates in FindDistributionParameters

I am trying to fit a non-standard PDF to data and FindDistributionParameters works great, and gives me the parameters of the distribution back using maximum ...
1
vote
1answer
91 views

Moment central of a binary image

I am implementing the Hu set of invariant moments detailed here Hu set of invariant moments. I implemented the moment Image like this: ...
1
vote
2answers
160 views

On Parameter Estimation using FindDistributionParameters

I am a novice of Mathematica and have recently started my self-study of maximum likelihood estimation (MLE) using Mathematica. I would like to estimate the parameters associated with a distribution ...
5
votes
1answer
332 views

Is there a free version of the Springer book “Mathematical Statistics with Mathematica”?

Is there a free version of the Springer book: $$\text{Mathematical Statistics with Mathematica}$$ by Rose and Smith ... available on the internet?
1
vote
1answer
105 views

Compute symbolic Expectation of a summation

I am required to computed following Expectations : $E[\displaystyle\sum\limits_{i=1}^N \frac{X_{i}}{N}] = \bar{x}_{0}$ & $E[\displaystyle(\sum\limits_{i=1}^N \frac{X_{i}}{N})^2] = ...
1
vote
2answers
97 views

Assign a Distribution to a group of symbolic variable [closed]

I'm looking to compute this Expectation : "i" represent a individual and h(i) is value. I would like the compute the Expected value of his value times the mean of the groups. Everything is unknown ...
0
votes
0answers
33 views

Chi square: compare two different distribution

I try to compare two file with two different distribution of numbers. So i have random1.dat and random2.dat each one are vectors of more then 1000 rows. I saw from this question Doing a chi-square ...
3
votes
2answers
289 views

KolmogorovSmirnovTest[] On Frequency Data

I have two observed frequency data, let say f1 = {100, 200, 150, 100, 50}; f2 = {110, 195, 160, 105, 40}; and i want to know whether these random samples belong ...
1
vote
3answers
72 views

Correct graphical representation of a discrete function (PMF)

I have a list: {1,2,2,3,3,3,3,4,4,5}. I want to plot the percentage occurrence of elements in the whole list. So the list plot I want to do is: ...
13
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 $x = W z+n$ ...
2
votes
1answer
91 views
1
vote
1answer
46 views

Replicability of RandomVariate within a function?

I have a rather basic question but can't figure out a foolproof answer. In the following code, I build a function which returns the mean difference between successive elements of a vector created from ...
0
votes
0answers
66 views

Undo differences in a time series

I have estimated and ARMA process in Mathematica using data which I have had to take the 2nd difference of to remove the trend. I have managed to fit a model to the detrended data but cannot work out ...
5
votes
1answer
233 views

How can we create a histogram distribution from binning data?

HistogramDistribution takes a list of data points, creates a histogram from them, and returns this histogram in a form that can be used as a distribution. I ...
3
votes
3answers
221 views

How to partition a list into sublists in a similar way to Histogram

I have a list of list as below (I show part of it) ...
8
votes
1answer
250 views

How does LocationTest choose its “AutomaticTest”?

Is there a way of determining how LocationTest chooses its "AutomaticTest"? Sometimes it's clear from the ...
4
votes
0answers
88 views

Given two samples, how does LocationTest select its AutomaticTest?

How does LocationTest select its "AutomaticTest" when testing two samples? Background: A previous post poses a similar question ...
0
votes
1answer
66 views

Loading Statistics`Library`

I need to use a number of functions from theStatistics`Library` namespace. Since that is a bit of a mouthful I would like to import it, but I get errors: ...
1
vote
3answers
121 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?
5
votes
0answers
207 views

Estimation of vector autoregressive (VAR) process

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