# Questions tagged [distributions]

A distribution is a mathematical description of probabilities or frequencies.

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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} ... 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. ... 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 ... 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 ... 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 ... 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 ... 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 ... 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)) ... 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_{... 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 ... 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\... 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 ... 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 ... 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 ... 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. ... 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 ... 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 ... 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? ... 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). ... 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 ... 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 ... 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 \}.$$... 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 ... 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 ... 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, ... 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 ... 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 ... 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 ... 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 \... 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, ... 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 ... 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 ... 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 ... 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 ... 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*... 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 ... 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 ... 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 ... 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 ... 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 ... 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 ... 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 ... 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: ... 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 ... 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 ... 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 ... 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 ... 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 ... 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(...
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 $Y_2$?