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Questions tagged [mathematical-statistics]

Mathematical theory of statistics, concerned with formal definitions and general results.

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30 views

An easy way to find the PDF of $XY/Z$

Suppose that we know the joint distribution $f_{X,Y,Z}$. I want to find the PDF of $W = XY/Z$ in a way that does not involve too much calculation. I have thought about first finding the Marginalized ...
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What is Importance Value?

I am reading this paper that talks about Principle Components analysis and Importance Values(IV) here Is this Importance Value a statistical concept? I could not find any information about it in ...
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Statistical test to verify if a population has a average of k times another

Consider the situation where there are 2 positive distributions with unknown expected values $\mu_1$ and $\mu_2$, We have samples $S_1 = \{x_1, x_2, ..., x_n\}$ and $S_2 = \{y_1, y_2, ..., y_n\}$. ...
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What is the intuition behind pi in the PDF of a Normal Distribution ? Is it related to some sort to a circle / sphere

The PDF of a Normal distribution is given as below I am aware of the various properties of Normal distribution and how the two parameters mu and sigma affect the shape of the distribution. What is ...
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Compute the information matries related to normal distribution

This is a problem that I have trouble with. Suppose that we have $X_{1}, \ldots, X_{m}$ are iid $N\left(\mu, \sigma^{2}\right), Y_{1}, \ldots, Y_{n}$ are iid $N\left(0, \sigma^{2}\right),$ the $X$ 's ...
126 views

Random variables $X, Y$ such that $X$, $Y$ and $\sqrt{X + \sqrt{Y}}$ belongs to the same family of distributions?

Is there a family of positive distributions such that if $X$ has the distribution in question, then $\sqrt{X}$ also has a distribution from the same family. Ideally, it would be great if $X+Y$ also ...
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Probability, Statistics [on hold]

1.Probability of getting two before three, 2. probability of getting 2 before 3 or 5 or 6, 3.probability of getting 2 before 3 or 4 or 5 or 6
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Outlier removal, extremes on both ends

A list of numbers and I want to remove the extremes on both ends. The standard deviation is calculated: 26.3 (rounded to 1 decimal) ...
14 views

Land Method for Lognormal Distribution

The Land Method is explain here. Anyone knows how I can look up the H*1-α* It says "Tables of these values are given by Gilbert (1987, Tables A-10 and A-12) and Land (1975). " Gilbert (1987) is not ...
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Product/SKU level time series forecasting [on hold]

Predict demand of product at each outlet for next 6 months 5 – 7 years of sales data at outlet level for each and every brand is available As it is a time series problem we need to design per outlet ...
14 views

Direction of a one sample Wilcoxon signed rank test

I am comparing a selection of values which come from a non-normal distribution to 0. I've done a wilcoxon in python: result = scipy.stats.wilcoxon(values) my W ...
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Range of integration for joint and conditional densities

Did I mess up the range of integration in my solution to the following problem ? Consider an experiment for which, conditioned on $\theta,$ the density of $X$ is \begin{align*} f_{\theta}(x) = \...
10 views

Is there an example that a probability distribution is having an increasing mean residual lifetime(IMRL) but not a Dreasing Failure Rate(DFR)

It is well known in risk theory that a random variable having a Decreasing Failure rate implies the Random Variable has an increasing mean residual lifetime. However, the converse is not true. Is ...
8 views

Which model is best using the hettest for heteroscedasticity test?

I have calculated hettest using STATA and i have found two models have no Heteroscedasticity problem. but i can not identify which one is the best model for my data. can you please help me out? I ...
35 views

What test should i use to prove A is better than B [closed]

I have sets of data that have number of goods produced by 2 machines, A & B for 2 months. Each machines has two numbers that is plan value and actual value. I'm not really familiar with hypothesis ...
69 views

Computing the confidence interval for two samples but getting slightly different answers

Consider two samples $X_1,..,X_k$ and $Y_1,..,Y_m$ where $X_i \sim \mathcal{N}(\mu_x,\,\sigma^{2})\,$ and $Y_i \sim \mathcal{N}(\mu_y,\,\sigma^{2})\,.$ Say $k=m=100$ and $k+m=n$. Say that the ...
87 views

Using all Metropolis-Hastings proposals to estimate an integral

Suppose we run the Metropolis-Hastings with target distribution $\mu$ to compute the integral $\int f\:{\rm d}\mu$. Usually, we use the estimator $$A_n:=\frac1n\sum_{i=0}^{n-1}f(X_i).$$ However, ...
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How to compute P values for Breusch pagan test?

I got bptest() output for my OLS model as follows; studentized Breusch-Pagan test data: modelfit BP = 3.3201, df = 3, p-value = 0.3449 I read that BP test is ...
11 views

Probability of random population value being higher than sample maximum

Considering a small sample size (n < 10) from a population, I'm trying to find how likely a random population value would be greater than the maximum of the sample. Hoping ye could help me with ...
49 views

linear combination and univariate normal

Show that $(X_1,X_2)$ has a bivariate normal distribution with means $\mu_1, \mu_2$, variances $\sigma _1^2$ and $\sigma _2^2$, and correlation coefficient $\rho$ if and only if every linear ...
26 views

What distribution can be predicted more accurately?

I am working on simple statistical prediction. However, whatever i did, i come up with a high range. I have used standard deviation and also percentile. Yes they work well in the given data but the ...
28 views

Determining between using Discrete vs Continuous Survival Analysis

This is a follow up question based on what has been explained here: Survival analysis: continuous vs discrete time but I wish to further confirm it for my case. I have a dataset collected over a ...
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Suggesting multiple labels prediction for multi-class training data

I have a dataset of tickets the machine gets for some machine components failure. The ticket are in text form. For each failure we have around 8-10 diagnosis labels. This tells what the issue might ...
26 views

Network analysis: Formal definition of the number of 1st order neighbours of degree 1

I am looking for a formal definition of a network metric I am using in a scientific article. Let $i$ be a vertex in a graph $G$ and $N(i)$ are the first order neighbors of vertex $i$. I am interested ...
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relation between location of a sample mean in sampling distribution and the standard error

Can someone explain the following statement with an example We'll describe the location of the sample mean by calculating how many standard errors it is away from the center of the sampling ...
47 views

How to compute confidence and prediction intervals for (nonlinear) regression using non squared “loss function”

Does somebody know (or can point me to a reference) how can I compute a confidence and prediction intervals for (posibly nonlinear) regression using non squared "loss functions"? Let me add some ...
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Which statistical test to use to compare 2 tests/measurements against a gold standard

I'd like to know how best to go about comparing 2 tests/measurements against a gold standard. Say I have 100 patients with 3D printed models and CT scans of their hands, and I'll measure a couple ...
Assuming that the elements of a 2x2 table (a,b,c,d) are binomial in distribution with a being $Bin(n_1,p_1)$ and c being $Bin(n_2,p_2)$. How can we show that \$\hat {var(logOR)} = \frac 1 a + \frac 1 b ...