# 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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### 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 ...
272 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 ...
901 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 ...
95 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 ...
208 views

### How to fit a Beta distribution to three estimates from an “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 ...
596 views

220 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 ...
114 views

### What is the meaning of monotone hazard rate (MHR) distribution?

It might be somewhat irrelevant to this forum but I think that many people here are familiar with this concept. I have seen that many papers assume that customers' valuation ($F$) is a monotone hazard ...
84 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, ...