A distribution is a mathematical description of probabilities or frequencies.

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What are the differences between stochastic v.s. fixed regressors in linear regression model?

If we have stochastic regressors, we are drawing random pairs $(y_i,\vec{x}_i)$ for a bunch of $i$, the so-called random sample, from a fixed but unknown probabilistic distribution $(y,\vec{x})$. ...
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1answer
15 views

What is the ideal distribution for a GLM for comparing survey data with election results?

I'm relatively new to statistical methods. I'm hoping to learn what kind of distribution I should use for some data I have. My dependent variable is the results a candidate received by county. My ...
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6 views

Can we obtain probability distribution of a repeatable event using Neural Networks?

We have a data where input of every sample corresponds to how many times a dice is rolled. The output is the sum of all the outcomes. For instance the data is ...
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1answer
22 views

Estimating R90 (radius of a circle expected to include 90% of impacts)

I want to determine how big a target I can hit with a bow at a certain distance with 90% probability. I place some paper targets at that distance and shoot 20 arrows at them. I have a ruler and a ...
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1answer
10 views

Use case for Anomaly Detection using the multivariate Gaussian distribution

We have 5000 vehicles of different classes (trucks, small cars, large cars) with 100 sensors in each car measuring fuel consumption, distance traveled, average speed etc for some time period $t$ that ...
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37 views

How do we obtain E(exp(C+By-Y'aY))?

How can I prove this ? I did get $B-2uA$ by identifying the $a+by+cy^2= -1/2 (y-u)^2/\sigma^2$ But, I don't know how to get $(2a+\Sigma^{-1})^{-1} \dots$ Am I missing something? A little help would ...
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64 views

Sample size for multinomial distribution

Suppose we have multinomial distribution with $k$ outcomes having the same probability $1/k$. What sample size do we need to guarantee with the probability $95\%$ that $m$ of the oucomes occur at ...
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1answer
37 views

Help Beginner Q: Explanation on pooled variance and when it is used

If I am conducting a difference in means hypothesis test, when do we use the pooled variance and why? Lets say the population variance was unknown for two samples, the sample sizes for the two means ...
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20 views

Jensen Shannon Distance Bounds

I am calculating and graphing various distances between probability distributions. I am really confused about the bounds of the Jensen-Shannon Distance. I read somewhere that the Jensen-Shannon ...
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1answer
59 views

How does the support of a continuous random variable change under transformations?

Let $X_1$, $X_2$ have a joint pdf and support set $S$. Suppose random variables $Y_1$, $Y_2$ are given by $Y_1=u_1(X_1,X_2)$, $Y_2=u_2(X_1,X_2)$ where the functions define one to one transformation ...
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14 views

Sample size for testing an output distribution

Please excuse the lack proper mathmatical notation. This is mostly from intuition about the underlying logic. Given a function $f(x)\rightarrow$ A or B randomly The function should return a ...
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5 views

How to translate theorem into R code properly? (ruin probability of a discrete-time bi-risk model) [migrated]

We're having trouble with the realization of this theorem (recurrence relation for estimating ruin probability of a discrete-time bi-risk model). Basically, here you can see the theorem itself with ...
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1answer
14 views

Probability distribution on a subset of a simplex

I want to define a probability distribution on a subset of a simplex. for example, on a 3-simplex, we know that $x_1+x_2+x_3+x_4=1$ and $X \sim Dirichlet$. Would it be possible to constraint $X$ more ...
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1answer
33 views

How can I determine the distribution of a statistic?

A similar question has been asked, but no answer was posted, so here I am again. I was doing a Likelihood ratio test and it yielded an ugly expression. Take this example: if $X$ is $B(n,p)$ ...
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1answer
47 views

Correlation of order statistics from Uniform parent

Can someone please help me out with this sum? It says: If $(X_1, X_2, \dots, X_n)$ are a random sample from Uniform(0,1) distribution, find the correlation between the order statistics $X$ ...
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15 views

Sum of two different probability functions [duplicate]

I'm have some problems estimating the marginal distribution from data. I found three different distributions that explain the data quite well: two log-normal (black) and one normal distribution (red). ...
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1answer
21 views

Does picking randomly from an imbalanced group balance the group?

If I had a bag of marbles with 75% blue and 25% red (ratio is what matters not raw number, so this applies to 100 marbles, 1000 marbles, 100000 marbles) So if I had this imbalance of 75% blue and 25% ...
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1answer
98 views

Age and residual life time of the Poisson process

Original Question Let $N(t)$ be a Poisson process with intensity $\lambda$. Let $T_1<T_2<...$ be the occurrence times. Let $T_0=0$. For any $t>0$, define the $age$ random variable to be ...
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3answers
132 views

Testing for specific normality in R

Is there a command in R, for which I can compare my specific sample to some specific (given) normal distribution? Like a qqnorm testing for the specific normal distribution ...
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7 views

Statistical difference between multidimensional sets

I have a set of models that produce a set of matrices (images) with certain features present (overdensities). However, the location of these overdensities change slightly between the models and I ...
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0answers
13 views

Given X a discrete random variable and a classification with probability p for group 1 and (1 - p) for group 2, what is the joint pmf? [closed]

So, my idea is that we have a discrete random variable $X$ with any distribution. Each value can be seen as the total amount, with the pmf the probability for this amount. We now separate this set ...
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1answer
37 views

Skewness for a sum of independent weighted bernoulli random variables with different probabilities of success

Suppose $Z_i$ are independent Bernoulli random variables with differing probabilities $P_i$. Also suppose weights $W_i$ are positive and constant. Let's define the random variable $S$ which is the ...
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7 views

Adjust data to some distributions [closed]

I have some data that looks like this: > str(nidd) 'data.frame': 154 obs. of 1 variable: $ Nidd: num 32.24 124.02 3.84 7.21 12.26 ... What should I do to ...
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5 views

Question regarding distributions and prediction

During my learning about distributions I came up with the following prediction algorithm. Given a dataset, for example a plot of stock prices to time. Select a range of values from the graph (for ...
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1answer
8 views

Residuals of SARIMA follow Student's $t$ distribution - implications?

I have fitted a SARIMA model to my time series. The diagnostics of the residuals are all good (ACF, PACF, ...), i.e. it seems they behave like white noise. But when I plot the normal qq-plot, they ...
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2answers
63 views

Student t-distribution parameter/s and MLE

So I always thought of the Student t-distribution as having only 1 parameter, v, the degrees of freedom (as described by wikipedia). When I searched however on how to find the MLE of v I keep coming ...
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1answer
28 views

Distribution of the product of a Wishart matrix

If $\mathbf{M} \sim W_2(\Sigma, 3)$ is a Wishart matrix and $\Sigma =\begin{bmatrix} 2 & 1 \\ 1 & 2 \end{bmatrix}$ then what is the distribution of $(3, 1) \mathbf{M}^{-1}(3,1)^T$ ? Thank ...
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46 views

How to properly initialize a stochastic vector?

I'd like create a stochastic vector $$\mathbf{v} = (v_1, \dots, v_n)$$ of length $n$, so that its elements are assigned weights according to a given parameter ("entropy"): the weights are either ...
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1answer
23 views

Finding outlier values for non-normally distributed data

I have univariate data (38 is the sample size).The distribution is certainly not normal. How can I find the outliers? I used z-score but am not getting a desired result.
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15 views

How to relate distributions?

I have 100 objects. Each object has 10 (highly correlated) attributes that I can measure. For each object, I obtain 10000 samples of that object's attributes. I now want to relate the attributes ...
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13 views

Distribution of Sum Square Total and Error in Textbook?

I'd like to check my understanding that there is an incorrect statement in my textbook. Then, I'd like to check my understanding on what is actually true. Montgomery's Design of Experiments textbook ...
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Find a threshold to seperate two distributions

I have two distributions, Number of students spent specified number of hours. One distribution for students who passed the exam, another is for those who failed. Now, I want to calculate a threshold ...
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30 views

How to measure extraneous and confounding variables?

The test-re/post/test methodology entails establishing a baseline, introducing a condition and measuring the effect size. The condition is known. But whether or not it yielded some changes, is what ...
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30 views

Find the most frequent timespan of event occurrence

I'm working on bike-robbery events dataset. I'm trying to figure out the most frequent timespan of a bike robbery. Most of time, the robbery does not occur when the owner is watching => the declared ...
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8 views

What kind of real world phenomena should fit Mielke's Beta-Kappa distribution?

I have a data-set for the concentration of 200+ metabolites measured from 180 different microbial samples. I was curious about what distribution I could best approach my data using scipy.stats. I ...
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21 views

Application of Anova/Manova

I have a dataset providing information about head and leg injuries for drivers and passengers . The dataset contains the following variables Head.IC: Head injury criterion(number) Chest_decel: Chest ...
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1answer
25 views

How can I analyze response data that is clustered around the ends and middle of a scale?

I have an experiment where I divide people up in to 4 conditions, give them 100 dollars and allow them to gamble any percentage of the $100 that they chose (50% chance of earning 2.5 as much as they ...
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15 views

How can I get the maximums in a set of data? [closed]

please excuse how janky the following graph I made is: x axis = number, y axis = frequency How can I obtain the maximums of a set of data similar to the one visualized above? I would want to ...
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3answers
24 views

fitting distribution with zero values [on hold]

Can I estimate the claim severity distribution with R if the data contains zero claims? or i must remove them from the data?
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1answer
37 views

Quantile and inverse CDF? [closed]

Since the cdf $F$ is a monotonically increasing function, it has an inverse; let us denote this by $F^{−1}$. If $F$ is the cdf of $X$, then $F^{−1}(\alpha)$ is the value of $x_\alpha$ such that ...
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1answer
20 views

Truncated distribution and mass points

If you have some continuous distribution $F(x)$ and you truncated the distribution at some inclusive point $m$ i.e. $F(x | x\ge m)$ does the truncated distribution have a mass point at $m$? Also ...
3
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1answer
100 views

The product of two lognormal random variables

Let $X_1$ and $X_2$ be two normal random variables. Write $X_1\sim N(\mu_1, \sigma^2_1)$ and $X_2\sim N(\mu_2, \sigma^2_2)$, to fix ideas. Consider the corresponding log-normal random variables: ...
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21 views

Why model data using parametric distributions instead of empirical?

I've been wondering why the use of empirical distributions in research is not as prevalent as I think it should be given my understanding (likely misinformed) that an empirical distribution would ...
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37 views

Probability theory and machine learning questions?

I'm reading Kevin Murphy's book Machine Learning: A probabilistic Perspective and while I was reading I ran into few problems like in this Image, in generative classifier, how do we get the right side ...
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138 views

How to extract distribution information from descriptive statistics?

In my thesis, I am trying to perform a Monte Carlo simulation with a set of parameters, where I take a random value from a known distribution to calculate a singe run of the simulation. However, for ...
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1answer
72 views

Why is a low (<1) chi-square measure unlikely when degress of freedom are high?

If the chi-square measures variability, where 0 is no variability and a very small measure is no variability, shouldn't all chi-square distributions be shaped like the dof-1 distribution, where the ...
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48 views

Does the product of three Gaussian random matrices converge in distribution to a Gaussian?

Suppose we have vectors $u,v \in \mathbb{R}^r$ with and matrix $W \in \mathbb{R}^{r \times r}$ where all entries of $u,v,W$ are iid $N(0,1)$. Does the following hold? \begin{equation} \frac{1}{r} ...
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1answer
21 views

Show that Weibull distribution belongs to a one dimensional exponential family

It is given that $f_\eta(y) = h(y)exp(\eta T(y)-A^*(\eta))$ $P_Y(y)= \frac{k}{\lambda} (\frac{y}{\lambda})^{k-1}exp(-(\frac{y}{\lambda})^k)$ What i did was by arranging $P_Y(y)$ to get ...
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2answers
57 views

What are the error distribution and link functions of a model family in R?

When building models with the glm function in R, one needs to specify the family. A family specifies an error distribution (or variance) function and a link ...
3
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1answer
63 views

log ratio of Poisson means versus logit of binomial probability

Assume that two observed counts C1 and C2 are independent realizations of two Poisson processes: ...