Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [distributions]

A distribution is a mathematical description of probabilities or frequencies.

1
vote
1answer
18 views

What is the expected value of half a standard normal distribution?

You have a normal distribution with mean of 0 and variance of 1. Keeping the same probabilities and focusing only on half of the distribution (other half has it's original probabilities but x values ...
0
votes
0answers
11 views

What is the discrete equivalent of a truncated normal? [on hold]

Let random variable X be distributed with a truncated normal with unspecified mean, unspecified variance, a(the lowest limit) = 0 and b some fixed natural number greater than 0. With the Y axis we ...
0
votes
0answers
3 views

What distribution/model should I be using for my data, and how can this be done in R?

In short, I am comparing how crabs heat up over time (every 5 minutes for 40 minutes), but in terms of sexual dimorphism (males have claws, females do not). I used 3D models and compared how a model ...
0
votes
0answers
14 views

Understanding the Cullen and Frey plot

I would like to figure out which distribution fits my data best. Here is the histogram of my data : I used the fitdistrplus package in R to try to find the best ...
1
vote
1answer
18 views

How can I compare how significant is the difference between three or more distributions of count data?

I am researching whether software developers use different numbers of communication channels when performing different activities. Therefore, I would like to know whether, depending on the activity, ...
0
votes
0answers
12 views

Are there any distributions where higher moments are defined but lower ones are not? [duplicate]

My assumption is that there is not (unless there is some playing around with inverse distributions). But are there any examples of distributions where ,say, the second moment exists but the first ...
2
votes
1answer
22 views

Theoretical dependency of moments on parameter of a Boltzmann distribution

Assume $$X\sim \frac{e^{-\beta Nf(x)}}{Z_{\beta}}$$ where $$ f(x) = -hx -x^2 + \frac{1}{\beta N}(1-x)\ln(1-x) + (1+x)\ln(1+x) $$ and $Z_{\beta}$ is the appropriate normalization factor. The support ...
0
votes
0answers
14 views

How to understand bayesian inference in the framework of deeplearning?

It is said that $p \left( \theta | y _ { 1 : N } \right) \propto _ { \theta } p \left( y _ { 1 : N } | \theta \right) p ( \theta )$. And $p \left( \theta | y _ { 1 : N } \right)$ is the posterior, $ ...
0
votes
0answers
7 views

Wilks' lambda's exact distribution when one of the parameters is 1 or 2

Citing Wikipedia, From the relations between a beta and an F-distribution, Wilks' lambda can be related to the F-distribution when one of the parameters of the Wilks lambda distribution is either 1 ...
1
vote
1answer
29 views

How can I make a Kolmogorov-Smirnov test to check if my data distribution is exponential?

I made a histogram of my data, and the fitting line, but from some reason the fitting line doesn't fit to my graph. How can I make it fit to it? How can I check if my data distribution is exponential?...
0
votes
0answers
14 views

Calculate total distance between multiple pairwise distributions/histograms

I am not sure about the terminology I should use for my problem, so I will give an example. I have 2 sets of measurements (6 empirical distributions per set = D1-6) that describe 2 different states ...
3
votes
1answer
212 views

Is Normal(mean, variance) mod x still a normal distribution?

Is the following distribution a still normal one? The range of values is constrained to hard limits $ \{0, 255\} $. And it's generated by $ \mathcal{N}(\mu, \sigma^2) \operatorname{mod} 256 + ...
0
votes
0answers
27 views

Minimal Sufficiency for Two Parameters [on hold]

Let $X_1, ..., X_n$ be iid $f(x; \theta, \lambda) = \dfrac{\lambda e^{-\lambda x}}{1-e^{-\lambda \theta}}$ for x $\in [0, \theta]$. I am asked to find I want to find A minimally sufficient ...
1
vote
1answer
60 views

Gamma distribution parameters estimation [on hold]

I have a set of samples taken from a population distributed with a Gamma distribution, so \begin{equation} f_X(x)=\frac{\beta^\alpha}{\Gamma(\alpha)}x^{\alpha-1}e^{-\beta x} \end{equation} I should ...
1
vote
1answer
42 views

Find UMVUE of $p^3$

Let $X_1, X_2, ..., X_n$ be a random sample from $Binom(1, p)$. I'm trying to find the UMVUE of $p^3$. Some thoughts: Apparently, $\bar{X}^3$ is not the answer, although it's the MLE of $p^3$. For ...
2
votes
1answer
44 views

Interval of confidence (for several tests)

Assume I am measuring the glycemic index with a blood glucose meter and its results fall within a $20\%$ range of real lab results. Example if the real blood glucose (BC) is $100$, the meter can ...
0
votes
0answers
5 views

ex-Gaussian analysis conceptual clarification

What would be an easy way to conceptually explain to someone what an ex-Gaussian analysis is? I could say that it is a convolution of a Gaussian and exponential distribution but I'm afraid that that ...
0
votes
0answers
11 views

How to Identify Nadir and Peak

I have the following data How can I identify the nadir and peaks of these two distributions? We know a priori these are two separate populations. Additionally, it appears that the first distribution ...
1
vote
0answers
18 views

Interesting and unusual dependent variable--how do you think it should be handled?

We have 2 dependent measures, which are both distributed from -4 to +4 in discrete steps. This is because the values are based on people's responses to four questions about whether they spend more ...
2
votes
1answer
33 views

Biased coins: Probability such that the first player throws heads

Let $A$, $B$ be the two players. Each one has a coin has a probability of getting heads of $p_i$. Player $A$ always starts first. What is the probability such that $A$ wins? Ex. The both coins land '...
3
votes
2answers
51 views

How to find the conditional CDF based on observed data in R [on hold]

If we have two samples (generally their distribution is not known),say $X\sim N(0,1)$, $Y|X\sim N(X,X^2/2)$. Can we recover the conditional CDF of $Y|X$ based on the observed samples in R? ...
0
votes
0answers
12 views

Particle Distribution Curves

I'll use aliases for my data it has clinical significance. Let's say I am counting white blood cells. These are in the 12-20 micrometer order but our only way of detecting them is using a "counting" ...
2
votes
1answer
17 views

Interesting variant on discrete probabilistic problem

Suppose $X \sim U(0,1)$ and $Y$ and $Z$ are random variables that depend on $X$. I've solved a problem where $Y$ and $Z$ are discrete (binary) and so finding the joint pmf just amounts to calculating ...
1
vote
0answers
22 views

If $X$ is from (canonical) exponential family, do we always know the distribution of $T(X)$?

Assume $X$ are generated by a distribution from exponential family, $$ f(X; \theta) = h(X)\exp\{\eta(\theta)T(X) - b(\theta)\}$$ After solving several exercises with various distribution functions, ...
0
votes
0answers
24 views

Simplification of bivariate normal $\phi_2(x,y,\rho)$ at $y=y_F$ (i.e. fixing one of the axes)

Suppose we start off with the traditional standard bivariate normal distribution: $$\phi_2(x,y|\rho,\mu_x=0,\mu_y=0,\sigma_x=1,\sigma_y=1)=\frac{1}{2\pi\sqrt{1-\rho^2}}\exp \left(-\frac{x^2-2\rho x y ...
0
votes
0answers
16 views

Survival analysis using a mixture distribution in R? [on hold]

I want to use a mixture of Gamma distribution as a parametric model for survival analysis on censored data using R. In the "flexsurv" package there are different distributions but I couldn't find a ...
1
vote
1answer
22 views

How to do “partial” survival analysis on randomly censored data?

Suppose that we monitor a population of devices over an interval $[a,b]$. Some devices are added before $a$ and some are added during $[a,b]$. Furthermore, some devices fail during $[a,b]$ and some ...
0
votes
1answer
19 views

Uniform distribution - proportion of times this person has to wait

I'm going over the teacher's solutions for a past homework assignment and I'm having trouble understanding the solution for one of the questions. I don't understand what the values plugged into each ...
0
votes
0answers
20 views

Basics of how to use fitdist function in R(from fistdistrplus package) [closed]

(I have a very basic understanding of how the fitdist function works,from what I understand it uses Max. likelihood estimation to estimate parameters such that the observed data could have come from a ...
2
votes
2answers
56 views

What is the probability distribution of linear formula?

What is the distribution name when probability values have a linear increasing of the form: $p(i)= \frac{2}{N(N+1)}i; 0 \leq i \leq N $
1
vote
0answers
13 views

Generate a sublist according to the probability distribution of a list

I have a list of elements with their frequency such as: A 3 B 5 C 7 D 8 E 11 Now I have to construct a sublist of size 5 out of the elements ...
0
votes
0answers
17 views

How is the response distribution chosen in “family” option of brm() function different from the posterior distribution? - brms [closed]

I am currently fitting a nonlinear multilevel model, using brms package. One of the options of the brm() function that I need to choose is "family", which, according to this is "A description of ...
0
votes
0answers
19 views

Correlation coefficients, many realizations [closed]

I'm doing an experiment to see the level of correlation between two variables $x$ and $y$. I simulated under the same conditions the set of data $x$ and $y$, and repeat it many times. After each ...
3
votes
2answers
66 views

Probability mass function for the first non-increasing sample from a random sequence

Consider a sequence of random numbers drawn IID from some distribution $g(x)$. How would I determine the distribution of the value of the first sample from that sequence which is not greater than all ...
2
votes
1answer
36 views

How to derive the joint distribution of Y=AX and Z=BX given a random vector X with known pdf?

Given a random vector $X \in \mathbb{R}^k$, with a known pdf given by $f_X$. If $Y, Z \in \mathbb{R}^k$ are defined by $Y = AX$, $Z = BX$, where $A,B \in \mathbb{R}^{k\times k}$ are different, given, ...
1
vote
1answer
26 views

Question regarding Extreme Value Theory and finding the distribution of X(n)

Hello stats stack exchange, I have a question regarding Order Statistics and the asymptotic distribution of $X_n$ which is the rv for max($X_1$, $X_2$,...,$X_n$) where $X_i$ are from some distribution....
0
votes
1answer
26 views

Fitting Log logistic and calculating its mean

I am trying to fit a log logistic curve to my set of data library(MASS) library(survival) library(fitdistrplus) library("actuar") ...
1
vote
0answers
11 views

create joint prob distribution or empirical relation for two variables

There are two variables, X1 and X2. The experimental study shows that they are highly correlated. Are there any reliable ways to create an empirical mapping(or equation) between X1 and X2. Assuming ...
0
votes
0answers
5 views

Multiple Response Frequency Table need help [closed]

I got this table of results for frequency of mortality categorized by year of death per age group. I need to have each age group also categorized by gender. I am using SPSS v.25. To get this table I ...
7
votes
2answers
578 views

Right-skewed distribution with mean equals to mode?

Is it possible to have a right-skewed distribution with mean equal to mode? If so, could you give me some example?
1
vote
0answers
18 views

How do I know which GLM family to use?

I have the following question: I need to specify the distribution, link function and linear predictor. I know how to do find the link function and linear predictor if I know the first but don't know ...
0
votes
0answers
8 views

how to check the distribution of the training set and testing set are similar

I have been playing the Kaggle Competition and I find there is a situation that the distribution of the training set and testing set are different, so I am wondering how to check the distribution of ...
0
votes
0answers
13 views

Seeking guidance on determining (predicting) probability (distribution) using Mixture Density (Neural) Networks

I work for an education PAAS (platform as a service) company helping colleges & training institutes manage their course evaluation and recruitment. Students can re-take tests multiple times, tests ...
1
vote
1answer
17 views

Accounting for membership in set, but also quantity in event

Say we have a sample space $$\Omega_1 = \{\text{"alpha"},\text{"beta"},\text{"gamma"},\text{"delta"}\}$$ if we only care about the (binary) membership in set in each event, the event space would be ...
0
votes
0answers
26 views

Bounding the KL divergence of a non-invertible transform of distributions

Let $p$ and $q$ be the distributions of random variables $x_1$ and $x_2$, and consider $p'$ and $q'$ to be the distributions of $g(x_1)$ and $g(x_2)$. For an invertible function $g$, it's true that ...
6
votes
1answer
70 views

Distribution of random variable with multinomial sampling distribution and parameters (𝑛,𝑝), where 𝑛∼ Poisson with truncation

Suppose you have: $$𝑋|𝑁∼\text{MN}(𝑁,𝑝_1,𝑝_2...𝑝_{J})$$ $$𝑁∼Poisson(\lambda)$$ What is the marginal distribution of $X$? In this case, the answer is simply this. But... Suppose further that ...
0
votes
0answers
17 views

Generalized logistic distribution

I saw on wikipedia https://en.wikipedia.org/wiki/Generalized_logistic_distribution that when $\alpha<\beta$, generalized type IV logistic distribution can be written as: $\frac{\exp(-\alpha x)}{(\...
0
votes
0answers
19 views

What is the posterior distribution of a Bernoulli prior that gets updated with a continuous uniform signal?

I'm trying to figure out what the distribution of the posterior is after I update a Bernoulli prior with a continuous uniform signal, say: P(D=G|u)=x where D{G,I} and u is uniformly distributed on ...
0
votes
1answer
35 views

Can I have some help for Statistics/probability theory

Let $\Omega = \{0,1\}^{\mathbb{N}} = \{\alpha=(\alpha_1,\alpha_2,...):\alpha_i \in \{0,1\}\}$ Fact. There exists a $\sigma$-algebra $\mathcal{F}$ such that for every $\beta = (\beta_1,...,\beta_n)\in\...
0
votes
0answers
5 views

Sufficient condition for existence of maximal/optimal coupling

Let us consider two random variables $X$ and $X'$ defined on the same measurable space $(E, \xi)$. Is there a sufficient condition on the distributions of the random variables $X$ and $X'$ for ...