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Questions tagged [geometric-distribution]

The geometric distribution is a discrete (count) distribution, where the probability of each count is a constant proportion of the next lower count. An example is 'the number of coin tosses until the first head'.

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26 views

Gaps in histogram for geometric distribution

I'm attempting an assignment in which we're supposed to write a function to simulate a geometric distribution with $p=0.03$. While plotting a histograms for about $100000$ simulations of the function, ...
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How to work out the expected value of $X^3$ for a geometric distribution

I have scoured all my textbooks and all through the internet but haven't been able to find a suitable answer to this. I have struggled my way through finding the expected value of $X^2$, with the help ...
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Variance for events occurring with gamma and geometric distribution

I am presented with a problem as follows: A listener is receiving messages with a wait time in between two consecutive messages that is exponentially distributed with a mean of 1 time unit. After any ...
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Proving that $\lfloor X \rfloor /n$ is a random variable and identifying its distribution. From Probability B. Fristedt

Let $X$ have the exponential distribution. For $n=1,2,\ldots$ let $Y_{n}$ equal $\lfloor X\rfloor /n$. Prove that $Y_{n}$ is a random variable, and calculate and identify its distribution function. ...
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Geometric distribution with a capped number of trials - finding expectation and prior predictive distribution

So I am modeling a random variable which follows a geometric distribution with probability $\theta$ except that the total number of trials is capped at some value $n$. I.e., the probability mass ...
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Interpretation of cdf of geometric distribution

Given a geometric random variable $X$ with $p = 0.05$, I want to find (for example) $P(X \gt 10)$. Trivially, this is $1 - P(X\leq10)$, which can be evaluated with the cdf as $1-0.4013$ or $0.5987$. ...
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Geometric distribution with multiple trials

Not sure how to word this question, sorry if it's dumb. But I was looking into geometric distributions to find the probability of the first success of some random variable X. So if p = 0.04, the ...
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Sum of a random number of r.v.'s [closed]

A fair coin is flipped independently until the first Heads is observed. Let the random variable K be the number of tosses until the first Heads is observed plus 1. For example, if we see TTTHTH, ...
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Geometric distribution with multiple success state and markovian succes probability

Let $X_t$ be a random process in the space $E:=\{F, S_1, S_2, S_3\}$ for each $t$. We can see it like it is a game where we can win in three different ways or we can fail. We play until we fail for ...
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Outliers on discrete data

Is there any robust methodology to identify outliers in the discrete data distribution. I am specifically concerned with discrete geometrical distribution? P.S. Data transformation does not seem to ...
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How much data is considered “sparse” for fitting a mixed (Beta Geometric) distribution with 4 shape parameters?

I'm using CamDavidsonPhillips Customer Lifetime Value library to calculate CLV, and it uses a distribution based on Peter Fader's work on the subject that fits a Gamma distribution to model customer ...
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Difference between geometric distribution and negative binomial distribution

How do I differentiate between a problem of geometric distribution and that of Negative Binomial Distribution? Both include something around first success or failure. I'm confused.
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Probabilistic user behavior markov models on web

I am considering the following probabilistic Markov model of actions of a user on the results page of a search engine. The user examines the first result, with a probability $A$ he is satisfied with ...
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Bayesian posterior for Geometric Distribution

I have the following homework problem I am trying to solve for but am stuck with the posterior part. Note the the geometric distribution is a discrete distribution that has a probability mass function ...
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Unbiased estimator of p in geometric distribution

The answer to this question given by my professor was statistic T(x)= 1when X=0 and T(x) = 0 otherwise. Can I consider E(x) = (1-p)/p and then cross multiply and take 1/(1+x) as an unbiased estimator ...
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How would I calculate a combination of the Binomial and Geometric Distributions?

To be specific with my problem, I'm calculating a formula for a game. There's 6 independent trials, each with an independent probability of success = 0.34. I know that from the Geometric distribution, ...
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Distances between random points in a hypercube and statistics of exponents

TL;DR: Why is $\text{avg}\left(|a-b|^k\right)=\frac{2}{(k+1)(k+2)}$? I.e. for $k=2$, as for finding average Euclidian distances, the result is $\frac{1}{6}$? I've been reading a book about "Corobs," ...
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Geometric distribution with random, varying success probability

I'm really sorry if this question is too basic, but I've been looking for a while and haven't been able to find a convincing response. My statistics background is rather poor. Geometric distribution ...
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Geometric Distribution - Biased Coin Flip

Whilst studying I stumbled on this problem, which I wish to check if my understanding is correct. Imagine we have a biased coin with probability 'k' of getting a head when flipped. Now A defines the ...
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Maximum likelihood estimate for geometric distribution from table

I am asked to compute the MLE of the parameter p of the geometric distribution and then apply it to some given data. It is easy to find the MLE: But how do I apply it to these data: ...
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Geometric Distribution

I'm trying to solve the following problem: The number of bombs required to achieve the disintegration is assumed to be geometrically distributed. In one series in which y bombs are available, x of ...
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How random variable $Y$ following geometric distribution in the following situation

I have a random variable, $X$ which follows exponential distribution with parameter $\lambda$. Then, define $Y=k$ for some $a$ greater than zero such that: $ka \leq X \leq (k+1)a$. Now, my ...
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Negative Multinomial Distribution as a sum of random variables

Given a random variable $x$ distributed according to a Negative Binomial distribution with dispersion parameter $r$, it can be seen as the sum of $r$ Geometric distributions. But given the Negative ...
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What is the probability that a best of seven series goes to the seventh game with negative binomial

Why cant we use negative binomial to calculate the probability of getting a 7th game in best of 7 game series? P(X=7, r=4) = {7-1 C 4 -1} * (.5)^(7-4) * (.5)^4 = .15 , so there is 15 % chance of 7 ...
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Confidence interval using Central Limit Theorem

I've been trying to find this information online, but have not had much success so far. I want to approximate the 95% confidence interval for the geometric distribution with the following parameters: ...
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Constant Curve for Cumulative Binomial

I am simulating traffic flow and have come across a rather interesting statistics problem that I'm having trouble wrapping my head around. I am modeling a stretch of road comprised of 2 lanes. Lets ...
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The special case of the negative binomial, the geometric and calculation with scipy

A particular case? One might consider the geometric distribution is simply a special case of the negative binomial with $N=1$. We know the geometric provides: "The probability the first occurrence ...
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Proof that the floor of an exponential random variable is a geometric variable

For any real number $x$,$[x]$ represents the smallest integer greater than or equal to $x$. If $X$ is an exponential random variable with mean $1/K$,show that $[X]$ is a geometric random variable with ...
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CRLB for estimating $\theta$ of $\sim\text{Geo}(\theta)$

I'd like to ask if the below computation of the information number for the CRLB is correct: Consider $x_1, x_2$ as iid $\sim Geo(\theta)$ Since $x_1, x_2$ ae iid and the geometric distribution is ...
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Expansion of Cumulant Generating Function of Negbin

Let $X \thicksim Negbin(r,p)$ where $(0\lt p \lt 1)$ I want to derive skewness and kurtosis of $X$ by getting the Cgf of X. First, since Followance of Negative Binomial equals to the distribution ...
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Expected duration of a conflict

I'm currently struggling with some statistical work, and thus I'm seeking your advice. I'm trying to investigate the expected duration of a conflict in a) a democracy and b) an autocracy. What I do ...
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If $Y$ ~ $geo(1-\theta)$, what's a ML estimator for $\theta$?

Suppose we have $Y$ ~ $geo(1-\theta)$ for $\theta \in (0,1)$. That is the pdf of $Y$ is given by $\theta^{k-1}(1-\theta).$ Formally, from what I understand the ML estimator for $1-\theta$ comes out ...
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Convolution of random variables: unimodality of the likelihood function

Let $X_1, X_2,...X_k$ be random independent variables, each $X_i$ drawn from a Geometric distribution $\mathcal{G}(p_i)$, and let its convolution, or sum, be $Y = \sum_{i=1}^k X_i$. The likelihood ...
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Total distribution of m geometric distributions

Suppose that you made a webpage and you are collecting the statistics from the visitors. There are m types of visitors (students, company recruiters, etc.). Each visit is equally likely to be any of ...
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Convergence in probability and distribution

Let $P(K=k)=(1-\beta)^k\beta ; k=1,2,3,...$ Then it is required to show $\beta K$ converges in distribution to an exp (1) random variable as $\beta$ tends to zero. For this they have started with ...
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Relationship between the binomial and the geometric distribution

I want to know the relationship between binomial and geometic distribution. I know the distribution both have two outcome and probability of success is the same for both distribution.