Questions tagged [probability-distributions]

For questions related to probability distributions, functions that relate a given value to the likelihood that a random variable will take that value.

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5
votes
0answers
54 views

What's the expected number of subsets of iid random variables with sum in given range? [closed]

Suppose $X_1,\ldots,X_n$ are drawn i.i.d from a uniform distribution on $[0,1]$ and let $x$ be the random vector $(X_1,\ldots,X_n)$. Then consider the random variable $Y_v = v^\top x $ for all $v \in \...
4
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1answer
57 views

Question about a queueing problem

Arrivals at a telephone booth are considered to be Poisson with an average time of 10 minutes between one arrival and the next. The length of phone calls is assumed to be distributed exponentially, ...
8
votes
1answer
180 views

Standard cumulative distribution function with optimization model variable

We all know that expressions in mathematical optimization models can't contain "black boxes" around a decision variable since everything has to be written using mathematical expressions. For example, "...
13
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1answer
186 views

Convexity of Variance Minimization

$X$ is a discrete random variable taking value $x_n$ with probability $1/N$ for $n=1, \ldots,N$. I would like to set the $x_n$ values in an optimization problem. My objective is to minimize the ...
11
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1answer
76 views

Model or State Uncertainty in Queueing Model due to uncertain arrival rate

Introduction I am currently modelling a scenario where two queues need to be served by a single server in a non preemptive discipline. I am quite sorted on generating the optimal policy via Value or ...
15
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4answers
753 views

Modeling the uncertainty of the input parameters

There are many approaches to deal with the uncertainty such as stochastic programming, robust optimization and fuzzy programming. Finding a suitable approach that is applicable in the real situations ...
4
votes
2answers
154 views

Queuing models in R, $\lambda$ Little

It's noted that the number of folks in a stationary system will maintain an average equal to the rate of arrival multiplied by the mean of the service distribution. The formula $L = \lambda w$ is ...
11
votes
1answer
166 views

How to fit a Beta distribution to three estimates from “expert”?

I'm modeling a process time, $X$, for a simulation study and have an "expert" estimate of the minimum, $\hat a$, the most likely (mode), $\hat m$, and the maximum, $\hat b$. I'd prefer to avoid the ...
9
votes
1answer
122 views

Loss functions for specific probability distributions?

For a random variable $X$ with pdf $f(x)$, the loss function* is defined as $$n(x) = \mathbb{E}[(X-x)^+] = \int_{x}^\infty (y-x)f(y)dy,$$ where $a^+ = \max\{a,0\}$. Or, for a discrete distribution, $...
12
votes
4answers
415 views

Normal demand and normal lead time; is lead-time demand normal?

In a continuous-review $(r,Q)$ inventory system under a type-1 service level constraint, if the demand per unit time is distributed as $N(\mu,\sigma^2)$ and the lead time, $L$, is a constant, then the ...