Questions tagged [distributions]

A distribution is a mathematical description of probabilities or frequencies.

Filter by
Sorted by
Tagged with
0
votes
0answers
9 views

Parametric model closed under translation, contraction, and maximum

Is there a nontrivial parametric model that is closed under translation, contraction, and maximum? That is, does there exist a nontrivial parametric model $\mathcal{M}$ such that $$\forall i (F_{X_i} ...
0
votes
0answers
24 views

Smooth sample space

What does it mean that a sample space is smooth and thus we can represent the target distribution with a probability density function? Source: https://arxiv.org/abs/1701.02434 in section "1. ...
0
votes
0answers
5 views

What stats distribution for predicting probability of an event reoccuring in the future? [closed]

I have many streams, where each stream contains a sequence of events happening in time. I want to model the probability of an event reoccurring, and also a distribution estimate of when the event will ...
0
votes
0answers
15 views

Trying to find errors in the distribution and the numerical summary of a graph of test scores

My mathematics and statistics instructor gave me a graph showing the distribution of test scores for exam 1. She said that there are errors in the numerical summary of the graph and in the ...
0
votes
1answer
18 views

How to estimate the PDF of the logarithm of a uniformly distributed random variable?

This is a question I have to solve and need help with. I know it's usual to give pointers and hints so the OP can follow from there. Thus, I'll appreciate all input that shows me the way to go. Let $...
0
votes
0answers
10 views

How can I make a probability paper plot of a log-normally distributed variable?

My company has software that can take a vector of samples and easily create a probability plot of the data and the least-squares or method of moments fit of the data. However, I need to be able to ...
0
votes
1answer
19 views

Convert Probability Density Function to Normal pdf

Suppose i have a variable that follows a certain distribution. For example $X \sim exp(\lambda)$. If a want to find $P(X > k)$, i just need to integrate the pdf between $k$ and $\infty$. Suppose ...
0
votes
0answers
10 views

How to evaluate the following probability? [closed]

Let us consider a probability of the form \begin{equation} P(\varepsilon_t+x_{t-1}<0) \end{equation} where $\varepsilon_t$ for $t=1,...,T$ are independent error terms (say distributed as $N(0,1)$) ...
1
vote
1answer
26 views

How to derive the distribution of a random variable as the absolute value of a uniform random variable

I'm trying to derive the distribution of a random variable $Y$ given that I know the distribution of a random variable $X$ and the relationship they share. The $pdf$ of $X$ is expressed as: $ f_{...
0
votes
0answers
7 views

Difference between pooled data or panel data for my situation

i am a beginner for panel data econometrics. Need help of experts of the field deciding if it is panel or pooled data or should i use any other methodology. I have data from wind mill and we use wind ...
0
votes
1answer
18 views

What is the probability that X=Y<Z

Let $f(x,y,z)=e^{-x-y-z},\,x>0,y>0,z>0$ and 0 elsewhere, be the joint PDF of (X,Y,Z). Compute, $P(X=Y<Z).$ I started the answer as follows. $\begin{align*} P(X=Y<Z)=\int_{z=0}^\infty\...
0
votes
0answers
9 views

Express the posterior distribution: $P(L|X_{1:N})$ using Baye's Rule in terms of the Uniform Distribution

$f(Z; A, B) = \frac{1}{B-A+1}$ if $A ≤ Z ≤ B$, 0 otherwise $(1)$ $P(L) = f(L; 1, M)$, (the prior) $(2)$ $P(X|L) = f(X; 1, L)$ (the likelihood of a single license plate number X) $(3)$ We further ...
1
vote
0answers
12 views

Probability of a binomial random variable being the maximum of a set of binomial random variables

Let $X, Y, Z$ be independent random Binomial variables, each parametrised with different $p_X, p_Y, p_Z$ but the same $n$. I am interested in a formula for determining the probability that the value ...
0
votes
0answers
12 views

In a statistics paper, how to know which parameterization of a given distribution is being used?

Let's say I'm reading a paper, and the authors write $\alpha \sim \text{gamma}(a, b)$. How do I know which parameterization of the gamma distribution they are using? Is there a convention or must one ...
0
votes
0answers
15 views

Fitting a distribution. How

First of all, i am not good at this. i need to know what distribution fits in this dataset. i though it could be a poisson due to the characteristics of the data. the data talks about forest fires. ...
0
votes
0answers
15 views

Probability of filling M boxes with 2 or more elements when sampling S elements from N total elements

Similar to this question, Frequency of Item in Combination. I am randomly sampling S objects out of N=99 objects into 9 boxes labeled by a single character, "A-I". Question 1: I want to find the ...
0
votes
0answers
10 views

Understanding NBD transaction process and Pareto dropout process plot conceptually

I am learning to use the BTYD package that uses the Pareto/NBD model to calculate CLV. However, I am struggling to understand certain plots conceptually. For ...
-1
votes
0answers
24 views

Generate a probability distribution given min, max and mean value in python [closed]

I want to create a long-tailed probability distribution given min, max and mean value. For eg: min=10, mean=15, max=1000 How can I create(simulate) such distribution and sample from it in python? ...
2
votes
1answer
28 views

Modeling the assembly of an icosahedral virus?

The capsids ("shell") of some viruses exhibit T=1 icosahedral symmetry. In short, this means they are assembled from 60 copies of protein subunits which form an icosahedron (a shape with 20 faces). ...
0
votes
0answers
15 views

How do I calculate the expected value of a binomial distribution for a genetics example?

I have model with 20 genes which can take on a value of 1 or 0 (the alleles). What is their expected value and variance assuming the alleles are selected with equal probability? Is this just a ...
0
votes
0answers
57 views

I'm searching for a sampling kernel capturing the idea of a small local perturbation (like the normal distribution does)

Let $d\in\mathbb N$. I'm searching for a Markov kernel $\kappa$ on $\left([0,1)^d,{\mathcal B([0,1))}^{\otimes d}\right)$ suitable for the following application: Given $x\in[0,1)^d$, I want to sample ...
1
vote
0answers
19 views

(Generalised) Negative Multinomial Distribution

Fix some probability vector $( p_1, \ldots, p_N)$, and let $X$ be a categorical random variable with these probabilities, i.e. $$P ( X = x ) = p_x \quad \text{for } x \in \{ 1, \ldots, N \}.$$ ...
0
votes
0answers
11 views

Comparing Discrete Lognormal Distributions

Is it possible to have the following: Create an approximation of the discrete lognormal distribution? Given a discrete distribution in the form of a histogram, is it possible to compare its ...
3
votes
1answer
84 views

In R, how to detect possible outliers in right skewed data assuming Poisson distribution?

I am attempting to identify possible outliers in data which is skewed to the right and I assume it is Poisson distributed. I am a novice in all things statistics, and the following may be utterly ...
0
votes
0answers
10 views

Having strange result on probability density function [closed]

I found out there was some difficulty while my project is going on. Hopefully request for consultation in order to complete my final year project and pass for my degree. With the attachment below, ...
0
votes
0answers
22 views

Calculating the probability distribution for Hardware defects based on history of defects

I'm writing a study about Hardware status in my institution. I've gathered data about hardware failures over time (I know how many failures happened each semester each year on a specific hardware ...
1
vote
0answers
16 views

Distribution of forecast error of ARMA + GARCH model

I am modelling a time series process and want to explore ARMA + GARCH. Using ARMA alone, with normally distributed residuals, we can determine the distribution of the forecast error using the ...
0
votes
0answers
25 views

Is there a way to check the independence of observations within a Poisson distribution?

I have the understanding that one of the key assumptions of a Poisson distribution is that the observations are independent. Is there a way of testing the independence of the observations within a ...
0
votes
1answer
20 views

Is there a probability distribution similar to Poisson, but with controlled variance?

Is there a probability distribution similar to Poisson, but with controlled variance? Poisson distribution with a lambda has a fixed mean and fixed variance; both mean and variance are equal to the $\...
0
votes
0answers
34 views

What would be an appropriate statistical test to compare two sets of distributions and prove one of them is left skewed compared to the other?

As the title states – I'm trying to compare two distributions that capture two same length time period before and after an event occurred. The hypothesis goal is to prove that after an event occurred, ...
0
votes
0answers
13 views

Imperfect test sensitivity…what does 0% prevalence really mean?

I'm trying to think about test sensitivity and specificity in a theoretical disease-host system. Say you have a population from which you take a sample and test for the pathogen of interest using a ...
1
vote
1answer
58 views

Is there any difference between these two terms, Population and Probability Distribution?

I am learning trying to learn more about statistics and probability theory, but I am having trouble understanding some of the terms that I feel have same or similar semantics just different name. For ...
0
votes
0answers
21 views

Is there a named distribution with the property $P(X>10^k) = p^k$?

If I'm doing my math correctly, the exponential distribution has the property $P(X >k) = p ^ k$ (with $p$ conventionally written as $e ^ {-\lambda}$). I'm wondering if there is a different ...
0
votes
0answers
25 views

How to come up with this error estimation? [duplicate]

I am trying to understand the answer to question 2 of a trajectory estimation. The vertical coordinate (“height") of an object in free fall is described by an equation of the form $x(t) = \theta _0 ...
1
vote
1answer
41 views

Prove that argmin of exponential distributions has multinomial distribution [closed]

Let's say we have $ T_1,T_2,\cdots,T_n \sim Exp$ and $P(X_1>a)=e^{-\lambda_1 a},P(X_2>a)=e^{-\lambda_2 a},\cdots,P(X_n>a)=e^{-\lambda_n a} $. How can I describe $\DeclareMathOperator*...
0
votes
1answer
26 views

Clarifying definition of Probability Mass Function (PMF)

I am currently reading Deep Learning book, and I want to get better understanding of probability theory. In chapter 3.3.1 of Deep Learning book it states that: Often we associate each random ...
0
votes
1answer
23 views

How can I generate 50 observations for discrete uniform distribution [closed]

How do I select a simulation for discrete uniform distributions.The question wants me to generate 50 observations and construct a frequency table using the inverse distribution function method and any ...
0
votes
1answer
39 views

Distribution of a binomial random variable multiplied by a constant

I'm trying to model a process in which a success is the generation of $2$ items. If I model the process using a binomial random variable with p equal to the probability of success, I can compute the ...
0
votes
0answers
6 views

Grouping categories of data to produce homogeneous distributions

Forgive me, university was a decade ago and my technical knowledge and language has faltered greatly outside of the elements I use regularly, but I'm hoping someone can help with the below. In ...
0
votes
0answers
18 views

Bootstrapped distribution of RMSE

I have two distributions of volume conservation factors (VCF) Generic and Generic Masked that I want to compare. The VCF being optimal if equal to 1, I want to show that one distribution is ...
0
votes
0answers
20 views

How to compute conditional probabilities when the condition not observed but a probability itself?

Suppose I have: A Markov matrix that describes the probabilities of transitioning from any one of 5 states to another, and A mixed model distribution for these 5 states that I can use to determine ...
2
votes
2answers
34 views

Low probability of a multinomial for expected values

given a population with 4 groups for which their frecuencies are: A = 0.46 B = 0.075 C = 0.035 D = 0.43 The expected number of individuals for each group in a ...
1
vote
1answer
33 views

Understanding the assumptions of a Poisson regression model? Modeling plant diversity

I have data on plant diversity in response to a fully crossed treatments of fertilizer and light in grassland systems: ...
1
vote
0answers
9 views

How to deal with a single biomarker measurement that is time dependent

Information: We measured about 50 biomarkers derived from 100 patients. There is only one time point at which the sample is collected. The samples were stored in the refrigerator until we analysed ...
1
vote
2answers
15 views

Sample Gamma distribution in R [closed]

I’m doing a programming assignment on sample gamma distributions in R. I used a loop to create histograms of a total of 49 different samples, each with different parameters. I was then asked to ...
0
votes
0answers
8 views

How to connect distribution selection and model selection in generalized linear models [duplicate]

I am trying to better understand the general process of choosing a distribution family and linear predictor for a generalized linear model. There are plenty of examples out there for specific data ...
8
votes
1answer
99 views

Why does R refer to the distribution family as an “error distribution” in the context of generalized linear models?

I was wondering why R refers to the distribution family as an "error distribution" in the context of generalized linear models? Normally distributed errors(residuals) of a fitted model are a key ...
0
votes
0answers
34 views

Relating $E[X]$ and $E[h(X)]$ by 'adjusting' the PDF

I have just started studying statistics and I have been introduced to PDFs and expected values. Now the formal definition of $E[X]$ for a continuous random variable is $\int_{\mathbb{R}}tf(t)\mathrm ...
0
votes
0answers
15 views

Let 𝑋 be a Log-Normally distributed RV with 𝜇 = 3 and 𝜎 = 2. Determine 𝐸[max(𝑋 − 100, 0)]

See the question above. I am not quite sure, if my result is correct, because I do not have any solutions. I tried with the following formula: $$ E[X] = e^{\mu+\frac{1}{2} \sigma^{2}} \cdot \Phi\left(...
0
votes
0answers
33 views

Distribution of function of random variables

Let $X_1$ and $X_2$ be an iid $N(0,1)$. Suppose that $Y_1=X_1^2+X_2^2$ and $Y_2=X_1X_2$. How to find the joint pdf of $Y_1$ and $Y_2$?

1
2 3 4 5
137