Questions tagged [discrete-distributions]
The discrete-distributions tag has no usage guidance.
89
questions
0
votes
0
answers
29
views
We have a 4 sided die, a 6 sided die and a 12 sided die. We roll a die twice and get 1 and 5. What's the probability that we rolled the 6 sided die?
I'm trying to solve this question but I'm not sure about my thinking.
So I think what I need to compute is : $$P[\text{rolled the 6 sided die} | \text{got numbers 1 and 5}]$$
I tried to do it with the ...
1
vote
0
answers
23
views
Confidence intervals for integer parameters
I'm interested, purely out of curiosity, in what methods can be used to calculate confidence intervals for discrete integer model parameters.
As an example, consider the model (which I can flesh out ...
8
votes
2
answers
366
views
Regression model for integer response
Let the response be $Y_i \in \mathbb{Z}$ and the covariate $X_i \in \mathbb{R}^p$. For counting data where $Y_i$ are restricted to be nonnegative, we have Poisson regression or negative binomial ...
0
votes
0
answers
13
views
Joint distribution of two discrete random sample
Assume $x_1$ and $x_2$ form a random sample from the following discrete distribution:
$ \quad x| \qquad 1 \quad 2 \quad 3 $
$\, P(x)| \quad .1 \quad .2 \quad .7 $
How can I find the joint ...
0
votes
0
answers
19
views
Ways to measure deviation from a discrete uniform distribution [duplicate]
I'm looking for a way to characterize the deviation from a discrete uniform distribution.
Example: 50 balls are distributed over 10 urns.
In the most equal case, all urns get 5 balls.
In the most ...
1
vote
1
answer
38
views
Construction of statistics of a discrete distribution
I have the following problem: we consider an i.i.d sample $\mathbf{X} = (X_1,...,X_n)$ of the discrete set $\{1,...,N\}$. An agent has to infer the probability distribution of $X_i$.
I wanted to use ...
3
votes
1
answer
35
views
Which is the correct solution to the hypothesis testing: $H_0 : \lambda =65, H_1 : \lambda >65$ , $X$ is a Poisson ($\lambda$) ,$\alpha=0.05$
Given the following hypothesis test:
$H_0 : \lambda =65, H_1 : \lambda >65$ , where $\lambda$ is the parameter of an $X$ distributed as a Poisson $\alpha=0.05$ . We have n=10 samples. Using as ...
1
vote
0
answers
31
views
How to validate the decomposed distributions?
I am fitting distributions for the time spent for three processes (i.e., pick up tools, walk to destination, install) in a system that I am trying to simulate where the original data for these ...
2
votes
2
answers
61
views
Showing that $E[\hat{\tau}_D] = P(n_D > 0)\tau_D$ and $\vert E[\hat{\tau}_D] - \tau_D\vert \leq \tau_D(1-\frac{N_D}{N})^n$
Consider the following double sampling scheme:
We have a population of size $N$ with variable of interest $y_i$ for each $i \in \{1,\dots,N\}$, and (fixed) subpopulation $D$ of size $N_D$. Let $S$ ...
0
votes
0
answers
3
views
What metric is best fitted for comparing encodings?
I am trying to compare two distributions, that each correspond to different numerical encodings, e.g. compare fp32 encodings to various other encodings on a same set of values.
However I do not know ...
0
votes
0
answers
13
views
Can we use Dirichlet process to simultaneously estimate the number of mixtures and component distribution of a Bernoulli mixture?
Suppose I have a random sample on a Bernoulli random variable $\{X_i\}_{i=1}^N$ generated from model $p=\sum_{k=1}^K\pi_kp_k$,where $p\equiv Pr(X=1)$ and $p_k\equiv Pr(X=1|k)$, and $\pi_k$ are the ...
11
votes
3
answers
685
views
How do you calculate the expected value of a discrete distribution without replacement?
Say I have a set of 10 values I want to draw 3 values from, uniformly, without replacement. For instance:
$$S = \{0,0,0,0,22.95,0,0,0,19.125,25.5\}$$
With replacement, this seems simple, you just add ...
1
vote
2
answers
67
views
Goodness-of-fit tests for discrete distributions
I have data where only values at large x should fit to a particular distribution whose parameters I wish to determine. I want to do a goodness-of-fit test to find the value of x where the data fit to ...
1
vote
1
answer
28
views
If hitting a target has $P = 0,3$, how many shoots to get at least one hit with a probability of $0.9$?
Cheers, I know that hitting a target has a probability of $0,3$, and I am asked to find the number $n$ of times that I have to shoot at the target to get at least one hit with a probability bigger ...
1
vote
1
answer
114
views
randomized Neyman-Pearson lemma for a discrete distribution
We let $\Theta=\{0,1\}$, and $X$ be a discrete R.V with the following probability distribution:
x
1
2
3
4
5
6
7
8
$f(x;0)$
0.02
0.02
0.02
0.02
0.02
0.02
0.02
0.86
$f(x;1)$
0.14
0.12
0.10
0.08
0.06
...
1
vote
1
answer
31
views
Distibution of the number of trials required to see all possible outcomes
In the simplest case given a set of N items is the distribution for the number of draws with replacement before all items are seen? This is the case I really need.
More generally what is the ...
0
votes
0
answers
38
views
KS test or chi square for comparing two distributions of a discrete ratio variable
I have a discrete ratio variable (length) from two samples and I'd like to know if the distributions are different or the same. In my case length is discrete because it can only take on integer values ...
1
vote
0
answers
47
views
Approximating a countable-state (infinite) Markov model with a finite-state one
TL;DR—in a nutshell
I have a countable-state Markov model (with a countably infinite number of states) in which the probability of transitioning to states $S_{i>k}$ for large $k$s are practically ...
1
vote
1
answer
81
views
Central limit theorem for independent, non-identically distributed, finite discrete random variables
I am positive, that there exists a version of CLT stating that, the distribution of the sum of infinite many independent, nonidentical, finite discrete random variables, is Gaussian. I just could not ...
3
votes
2
answers
193
views
Sampling from a Poisson distribution (infinite support)
I would like to sample from an infinite discrete distribution, i.e. Poisson distribution
\begin{align}
\Bbb P(X=k)=e^{-\lambda}\frac{\lambda^k}{k!}
\end{align}
where $\lambda$ is a fixed parameter.
In ...
0
votes
0
answers
40
views
Probability of independent transmission attempts (independent Bernoulli trials)
I am trying to figure out the independent transmission attempts (independent Bernoulli trials) probability $q$ for a sender node to remain in the same (waiting) state if receiving node is in sleep ...
1
vote
1
answer
28
views
How to random generate a sample from {0,2} in R? [closed]
There are some solutions online on how to do a random generation of the discrete uniform distribution, but only on consecutive integers. Like :
...
0
votes
1
answer
75
views
How to solve the probability of N events occurring at the same time, N is a random variable [closed]
How to solve the probability of N events occurring at the same time, N is a random variable and its PDF is known. The probability of each event is also known and the probability of each event is not ...
0
votes
0
answers
38
views
How to calculate the variance of drinks orders?
I'm taking a stats course on LinkedIn's learning site and they provide this problem. Calculate the variance of the drinks orders in the following table. The idea being to figure out the variance of ...
1
vote
1
answer
63
views
Joint PMF of two order statistics with discrete parent distributions
Let $X_1, X_2$ be i.i.d from a discrete distribution with finite support with cumulative distribution $F(x)$ and probability mass function $f(x)$. Let $X_{1:2}$ and $X_{2:2}$ represent the order ...
3
votes
1
answer
89
views
What is the distribution of the difference of two independent multinomial random variables?
Say I have two independent random vectors $X_c$ and $X_f$.
The random vector $X_c$ is composed by three random variables: $X_{1c}$, $X_{2c}$ and $X_{3c}$. The second random vector $X_f$ is composed by ...
1
vote
1
answer
33
views
Odds that 5 persons share the same last name given a group of n people
What are the odds that 5 individuals share the same last name, say Miller, in a group of 50 assuming the associated probability of 'Miller' in a population being 2%.
How do I calculate it? Thought ...
1
vote
1
answer
56
views
Variance of discrete distribution exceeds variance of discrete uniform distribution
I am not a mathematician, so I don't quite understand how comes that a variance of some discrete probability distribution could exceed the variance of the discrete uniform distribution. I thought that ...
1
vote
0
answers
8
views
How to measure degree of groupings
I have a set of boolean data where I'm trying to distinguish between data where the values are uniformly distributed and data where the same class is grouped together.
e.g 1001010011 seems pretty ...
0
votes
0
answers
26
views
How to generate uniformly distributed random numbers between 1 and 26 with a dice [duplicate]
I want to generate uniformly distributed random numbers between 1 and 26 with a dice: Is this correct:
I have assembled the following algorithm using the Monte Carlo Method:
{1, 2, 3, 4, 5, 6} {7, 8, ...
0
votes
1
answer
31
views
Probability of not picking a row in a random draw where the number of rows are N
There are $N$ rows :$R_1, R_2,R_3,..., R_N$. What is the probability of not picking a row in a random draw?
My try and understanding :
Let $X$ be a random variable which is defined as follows:
$$X = \...
0
votes
1
answer
106
views
Why aren't Normalizing Flows suitable for Discrete Distributions?
I am currently trying to understand why normalizing flows are not applicable to discrete distributions (a quick primer on NF can be found here).
The assumptions on the transformation f between the ...
1
vote
0
answers
29
views
Multi-Multi-Class Classification
I'd like to build a model that can output results for several multi-class classification problems at once. Suppose you have diagnostic data about a product that needs to be repaired and you want to ...
4
votes
0
answers
104
views
distribution bootstrap sample median
I am interested in the conditional probability that the median $X^*_{(m)}$ of a bootstrap sample $X_1^*,\ldots,X_n^*$, where $n=2m-1$ for integer $m$, equals the $k$th order statistic $X_{(k)}$ of the ...
2
votes
2
answers
80
views
Approximating non-integer median for CDF of discrete variable
In my googling, it seems the proper way to find the median of a cdf of a discrete variable is to stick to the discrete values provided, even if you overshoot and end up with an x where P(X <= x) &...
2
votes
1
answer
45
views
The Description of the Variable of Interest: Binomial VS Negative Binomial Discrete Random Variables [duplicate]
Does it makes sense to say that:
In a binomial distribution we looking for the number of successes in a given number if trials, and in a negative binomial distribution we are looking for the number of ...
2
votes
0
answers
22
views
Need help choosing which random variable distribution to use
I have these two questions.
A department store claims that 80% of its customers pay their credit card on time. If you want to calculate the probability that at least 6 out of 11 customers pay their ...
3
votes
2
answers
1k
views
Kernel Density Estimation for a Discrete Variable
I was tying to estimate the distribution for a discrete variable.
However, suddenly I thought that "Is a simple histogram sufficient? because I have observations for every evaluation point"
...
1
vote
1
answer
24
views
Test whether probabilities of heads are under-estimated across many coins
I am trying to figure out a problem that is equivalent to the following. Suppose you have a bag of $n$ coins in which each coin is labelled with a probability $p_i$ that it will come up heads when you ...
0
votes
0
answers
38
views
How to assess if a distribution has significantly changed over time
I'm studying the incidence of different types of influenza in a country over several years. In particular, for years from 2015 to 2020 I know the relative abundance of 3 types of influenza (% of ...
1
vote
0
answers
26
views
I don't need a full solution but i need guidance for the solution [closed]
I don't need a full solution but I need guidance for the solution.
0
votes
0
answers
50
views
MLE and binary variables
Suppose $z$ and $y$ are discrete random variables taking values 0 or 1. The distribution of $z$ and $y$ is given by $$P\{z=1\}=\alpha$$ $$P\{y=1|x\}=\frac{e^{\gamma x}}{1+e^{\gamma x}}\\ z=0,1$$
Here $...
1
vote
1
answer
34
views
What is the name and formalism of this discrete distribution? [closed]
I am searching the name of something similar to a binomial distribution, but with individual probabilities (P(1) to P(N)).
I calculated (brute-forced with a script) the probability of k positive ...
0
votes
1
answer
54
views
What distribution is $P_X(x \mid K, N) = \frac{1}{ ( 1 + N)^K} {x + K -1 \choose x} \left( \frac{N}{1+N}\right)^x$?
What kind of distribution is the following:
$$
P_X(x \mid K, N) = \frac{1}{ ( 1 + N)^K} {x + K -1 \choose x} \left( \frac{N}{1+N}\right)^x
$$
and how can I find $P_X(x < x_0 \mid K, N)$?
0
votes
0
answers
50
views
Test for null hypothesis: the rank of each variable is uniformly distributed
Assume the following situation:
I have $N$ samples of $k$ continuos variables, $$x_n = (x^n_1,...,x^n_k).$$
I do not trust whether I can combine the continuos variables across samples, but I want to ...
3
votes
1
answer
78
views
Expression for Probability of Being Between Two Poisson Random Variables?
I have two independent Poisson random variables $A \sim \text{Poisson}(\lambda_A)$ and $B \sim \text{Poisson}(\lambda_B)$. For a fixed given integer $k$, I'd like to determine
$$P(A < k \leq A + B)....
3
votes
0
answers
59
views
How to prove or disprove that a complete sufficient statistic exists?
We have a discrete random variable which takes values with probabilities $p, q, p+q$ and $r$. I want to construct a complete sufficient statistic based on a single observation from this distribution, ...
4
votes
1
answer
53
views
Finding the mode given the probability of occurence
When a teacher asks a question, a student has a probability of 0.4 of being asked. Assume the occurrence is independent.
What is the mode of the number of questions raised by the teacher it takes for ...
2
votes
1
answer
27
views
Does $ \sum_a P(a|b,c)P(d|a) = P(d|b,c)$?
I saw it applied in a textbook once, but can't seem to figure out why or if it holds.
2
votes
1
answer
82
views
Convolution of probability mass functions (3 non-parametric distributions)
I am familiar with the convolution of probability mass function when it involves two random variables, but I get a little confused when there's a third one.
I have to find the probability mass ...