Questions tagged [distributions]

A distribution is a mathematical description of probabilities or frequencies.

Filter by
Sorted by
Tagged with
0 votes
1 answer
11 views

Find pdf of X+Y

Let X ∼ Exp(λ) and Y ∼ Exp(μ) be two independent exponential random variables, where λ, μ > 0. Find the probability density function of X + Y if λ ̸= μ. I have successfully find ans if λ = μ, but ...
user avatar
  • 1
1 vote
1 answer
15 views

Binary Classification Problem with Predicted Probabilities distribution skewed

I have a balancedrandomforest model which was trained on unbalanced data (92/8) for a binary classification problem. The AUC is around 0.98 and the precision and recall are also acceptable being 0.89 ...
user avatar
0 votes
1 answer
22 views

Betting on a sample from a known distribution

This was an interview question. Given a known distribution, sample a value from it with replacement for many times. Two people A and B bet on the sample with their own guesses, and the one closer to ...
user avatar
  • 1
-3 votes
0 answers
17 views

"Consensus" on Analyzing Mixed Continuous and Categorical Data in the field of Statistics? [closed]

I have been trying to determine the popular "consensus" as to how mixed continuous and categorical data (e.g. a dataset that has variables on income and gender) is generally analyzed in the ...
user avatar
  • 5,698
0 votes
0 answers
14 views

How can I get an MME of negative multinomial distribution?

I know there is an MME(method of moment estimator) of negative multinomial distribution on Wikipedia (https://en.wikipedia.org/wiki/Negative_multinomial_distribution). However, the process of ...
user avatar
  • 11
0 votes
1 answer
28 views

how to generate data from beta-Liouville distribution?

I want to test my model following the beta liouville distribution, so as a synthetic data, I need generate data from this distribution. can anyone mathematically tell me how to calculate it? this is ...
user avatar
0 votes
0 answers
24 views

Find asymptotic variance of the moment estimator

I have that $$f(x)=\frac{1}{\sqrt{2 \pi}}e^{-\frac{1}{2}x^2}$$ I have the conditional distribution: $$f_{\beta}(y|x)=\frac{1}{\sqrt{2 \pi}}e^{-\frac{1}{2}(y-\beta_0-\beta_1x-\beta_2x^2)^2}$$ and we ...
user avatar
  • 253
0 votes
0 answers
50 views

If Y is the sum of normalized multivariate pareto random variables then Y is a Feller-Pareto random variable

If we let $\underset{k\times 1}{\boldsymbol{X}}=(X_1, \dots, X_k)' \sim MP^{(k)}(\boldsymbol{0},\boldsymbol{1}, \alpha)$ where MP denotes a Multivariate-Pareto distribution, with joint survival ...
user avatar
0 votes
0 answers
30 views

Skewed distributions: choosing the median or average

Goal: To determine whether to use the median or average (or a weighted combination of the two) from a data set based on whether ...
user avatar
  • 101
3 votes
1 answer
75 views

Usefulness of KS tests and other similar distribution comparing tests

I am working on a machine learning binary classification problem. I have an outcome variable status called as loan paid and <...
user avatar
  • 1,780
0 votes
0 answers
8 views

QQ Plot help meaning [duplicate]

How can I interpret the following QQ Plot? Can you explain it for example for the point 20 and 12?
user avatar
  • 1
0 votes
0 answers
22 views

Given two sequences of random variables whose moments match, does their difference tends to 0?

Suppose you have two sequences of random variables $(X_n)_{n \in \mathbb{N}}$ and $(Y_n)_{n \in \mathbb{N}}$ and you know that for every $n$ $$ \mathbb{E}[X_n^r] = \mathbb{E}[Y_n^r] \quad \forall \, r ...
user avatar
  • 1
0 votes
0 answers
14 views

If X follows the distribution with pdf $f\left(x\right)=\theta x^{\theta-1}\ $, prove that the distribution of $\mathrm{\Sigma}\log{x_i} $ is Gamma [closed]

I am trying to get log(x) to be exponential but I can't do it. Any help will be appreciated.
user avatar
  • 1
2 votes
1 answer
46 views

Prove $P(X_1+X_2> 2C) \leq P(X_1>C)$ if $X_1,X_2$ are identical, but dependent?

If $X_1,X_2$ are dependent but identically distributed, it seems obvious that $P(X_1+X_2\geq2C) \leq P(X_1\geq C)=P(X_2\geq C)$. At least if we additionally assume that the joint distribution is ...
user avatar
  • 23
0 votes
0 answers
28 views

Can you help me with distribution/Skewness

Can you tell me if the data normal distributed are? It looks a bit strange. I would say it is skewed 40,80 and so on are sizes of the Apartments in m^2
user avatar
  • 1
0 votes
1 answer
37 views

Distribution of the Spearman rank correlation coefficient under the assumption of non-zero correlation

There are some papers and some R packages providing exact calculations for the CDF and the inverse-CDF of the (sample) Spearman rank correlation coefficient. My question is: How difficult would it be ...
user avatar
  • 649
0 votes
0 answers
14 views

I tried to solve this problem but got stuck in the end - Sampling distribution

This is a problem about sampling distribution that got me a little confused.. The time it takes for students to complete their university degrees has a distribution normal mean 6,4 years and standard ...
user avatar
  • 1
0 votes
1 answer
34 views

Methods for modelling distributions?

As predictor X I have particle size distributions and I would like to run a model y ~ X. I.e. each trial has a response ...
user avatar
  • 115
11 votes
4 answers
810 views

What distribution to sample X from to get an uniform distribution in Y?

I have a random variable $X$ which is related to another random variable $Y$ as $Y = \text{cos}(X)$, where $X \in [0, \pi/2]$, and I would like to know what distribution I should sample $X$ from in ...
user avatar
  • 185
4 votes
3 answers
94 views

How to convert percentage values from 7 point scale to 5 point scale?

Suppose in one year I had a survey with 7-point scale and the values are like ...
user avatar
0 votes
0 answers
31 views

Deriving the CDF of student $t$-distribution

I am trying to derive the cumulative density function(cdf) of $t$-distribution, define as in https://en.wikipedia.org/wiki/Student%27s_t-distribution#Cumulative_distribution_function I derive it by ...
user avatar
1 vote
1 answer
56 views

Studying extreme value r.v. $X=\max_i (c_i+X_i)$ where $c_i$ are constants and $X_i$ are i.i.d. r.v

Let $X_1,X_2,...,X_n$ be independently and identically distributed random variables according to a distribution $F$. There are constants: $c_1,c_2,...,c_n$. Define a new random variable $X=\max_i(X_i+...
user avatar
  • 143
2 votes
0 answers
37 views

Test uniformity after adding some non-uniform data in python

I generate N1 numbers from uniform distribution using numpy python package from a certain interval e.g., ...
user avatar
  • 121
0 votes
1 answer
53 views

Normal Distribution or Not

I have some net yield data (N=700) from a survey and I intend to carry out analysis to identify if there is any significant difference or relationships between the yield and the characteristics of the ...
user avatar
1 vote
2 answers
49 views

Questions the calculation of Z score and confidence intervals in biology

In biology, especially in some screening assays, people love to calculate a Z score between positive and negative controls. Essentially a distance calculation using the mean and sd to calculate how ...
user avatar
  • 113
-1 votes
0 answers
29 views

computing the expectation of a variable

I'm trying to run a simulation but before I need to compute the exact value of X, where: V ~ Bernoulli(0.5) X|V ~ Normal(1-2 V, 1) The question is : what is the expectation of X (E(X)) in the ...
user avatar
1 vote
1 answer
33 views

Shapiro Wilk test of normality

I ran my data under JASP and the p-value for the shapiro wilk test of normality was <.001. How do I interpret this?
user avatar
  • 11
0 votes
0 answers
14 views

Return levels GEV distribution?

I am studying extreme value theory and I have a problem with the return level graph. I don't understand the convexity of the curves as a function of the sign of the shape parameter. In the book "...
user avatar
1 vote
0 answers
17 views

Visualization of $L(X)$

Let $L^2_+$ the set of all $2$-dimensional nonnegative random vectors $X = (X_1, X_2)^⊤$ with finite and positive marginal expectations, and let $Ψ^{(2)}$ the class of all measurable functions from $\...
user avatar
  • 111
0 votes
0 answers
20 views

How to find expected value from cumulative distribution function?

Hello everyone, I'm currently doing research based on the model in Competitive fit-revelation sampling and mixed pricing strategy (Wu &Deng, 2021). And I don't understand how they can conclude the ...
user avatar
2 votes
2 answers
401 views

Universal approximation of Gaussians

Can gaussian kernels reproduce non continuous L2 integrable functions? ( Do non continuous L2 integrable functions lie in the RKHS constructed by a Gaussian Kernel?) Edit: I think my question is being ...
user avatar
  • 65
0 votes
0 answers
12 views

Winning Bid probability [duplicate]

I had asked this question earlier, but I guess I was too late to respond to the questions. Hence reposting. Top 10 win probabilities I have a task at my hand to create some kind of model that can help ...
user avatar
7 votes
1 answer
122 views

Sample uniformly from unit square conditioned on sum and product

Consider the following conditional distributions: \begin{align} X, Y \stackrel{\text{iid}}{\sim} U(0, 1) &\mid X + Y = a & a \in [0, 2] \\ X, Y \stackrel{\text{iid}}{\sim} U(0, 1) &\mid X ...
user avatar
  • 913
2 votes
2 answers
70 views

Question on solution of Casella and Berger Exercise 9.10: Showing that $Q(t,\theta)$ is a pivot

My question concerns Exercise 9.10 of Statistical Inference by Casella and Berger: On page 428 the authors say In general, suppose the pdf of a statistic $T$, $f(t|\theta)$, can be expressed in the ...
user avatar
1 vote
0 answers
19 views

How general is this property about correlation and the sum of two normal RVs?

(Cross-posted from math stack exchange as I didn't get any responses there) Given a random vector $(X_1,X_2)$ that is jointly normal with means / sd's $\mu_1,\mu_2, \sigma_1,\sigma_2$ and correlation ...
user avatar
  • 11
0 votes
1 answer
18 views

Statistical methods for different parts of a distribution

I have a distribution of discrete values (grades, from low to high) where I see that the certain groups have a higher frequency of observations in the higher ranges and less in the lower ranges than ...
user avatar
  • 3
3 votes
1 answer
33 views

Estimate parameters of an unknown negative binomial distribution based on known distribution

The PDF of a known NBD given in Equation (1). The parameter a and r are function of $μ$ = sample mean, and $s^2$ = sample variance, as given in Equation (2) and (3) respectively. $r$ = number of ...
user avatar
  • 131
0 votes
0 answers
11 views

Finding an optimal split of a sample, based on distance of sub-sample's empirical distributions

Consider a sample $X$, consisting of $n$ observations that are independent (but not necessarily identically distributed), as well as two splits $S_1 := (X_{1,\dots,i}, X_{i+1, \dots, n})$ and $S_2 := (...
user avatar
1 vote
1 answer
32 views

Get probability distribution function from density function and calculate the cumulative value [duplicate]

For the given density function, how to find its distribution function and how to calculate the value of the distribution function? Density function: $$f(x) = \frac{1}{\Gamma(\frac{n}{2})}x^{\frac{n}{2}...
user avatar
  • 19
0 votes
2 answers
81 views

Find the probability of which sample comes from a "higher" distribution based on random sample from two distributions

I am trying to find the answer for the following question. I have two distributions of numbers between 1 and 8, as illustrated here: I draw random samples from each distribution, which we can call &...
user avatar
  • 53
0 votes
0 answers
46 views

Top 10 win probabilities

I am a newbie here, hoping to find the right response for my question. I have a task at my hand to create some kind of model that can help me to determine what is the chance of winning a certain ...
user avatar
1 vote
0 answers
18 views

Methods to handle an arbitrary peak within a distribution

I had someone come to me for advice on how to deal with their weird data. The predictor variable is categorical (experimental condition), and the outcome variable is continuous (amount of money in a ...
user avatar
0 votes
1 answer
26 views

Infinitesimal Robustness, influence function of $T$ at $F$

This text is taken from Introduction to robust estimation and hypothesis testing. Wilcox R. First I will write down the description that leads to definition of relative influence on $T(F)$ and then I ...
user avatar
0 votes
0 answers
17 views

Fermi-Dirac Statistics and Maxwell-Boltzmann Statistics

Answer to question (b) relates to Maxwell-Boltzmann statistics. But how to show that the probability of each distinguishable distribution is $n*N^{-r} ?$ Each distinguishable distribution have equal ...
user avatar
2 votes
1 answer
69 views

n-th quantile for bivariate variable

I generate a 2000 bivariate random samples which are negative correlated. I used np.quantile to generate 10 quantile from this random samples. The related point is marked in the following figure. I am ...
user avatar
  • 1,127
2 votes
1 answer
63 views

Combinations from different sets with weightings

Imagine the following scenario: I want to create 1000 unique combinations of clothing. The combinations would include the following categories: hats, shirts, shorts, socks and shoes. Each combination ...
user avatar
  • 23
3 votes
1 answer
75 views

Determining distribution based on first three even moments

Given that $E(X^2) = 1, E(X^4) = 3, E(X^6) = 9$, determine all possible distributions of X. I'm sure there's some insight I'm missing here. I noted that X is mesokurtic, so it's possibly normal... but ...
user avatar
  • 155
1 vote
1 answer
42 views

Describing / fitting a highly skewed distribution

I've got a data set of 84,529 entries, each entry referring to the number of times a particular entry is cited in a database. This set is extremely skewed, ranging from entries with 0 citations to one ...
user avatar
  • 217
0 votes
0 answers
15 views

Calculating probability from first principles (modelling real world complex events)

I am watching this video on YouTube, as part of a gentle refresher on prob and statistics (I have a Postgrad degree in the field, but haven't used it for a while - so I am not a complete beginner). I ...
user avatar
0 votes
1 answer
38 views

Log-normal mean and standard deviation change after sampling

I have the log-normal standard deviation and the mean that I want to use to sample from a log-normal distribution in Python. However after I do the sampling and compute the arithmetic mean and ...
user avatar

1
2 3 4 5
175