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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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4
votes
1answer
46 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
173 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
votes
1answer
133 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
votes
1answer
74 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
votes
3answers
657 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 ...
3
votes
2answers
124 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. Where the formula $L = \lambda w$ ...
9
votes
1answer
125 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
115 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, $...
10
votes
3answers
322 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 ...