# 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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### 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 ...
83 views

### Markov Chain - Stationary or Borderline distribution [closed]

I have a Markov chain problem below, where : The problem An urn initially contains 3 black balls and 1 red ball. The balls are indistinguishable to the touch. One ball is randomly drawn. If this ball ...
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 ...
69 views

### How to calculate Cycle & Safety Stock

I have been asked to calculate cycle and safety stock levels for one of our business units. I have very little/no knowledge on the subject of inventory theory so would like to ask what a reasonable ...
120 views

### Convexity of the variance of a mixture distribution

$X$ is a random variable that is sampled from the mixture of uniform distributions. In other words: $$X \sim \sum_{i=1}^N w_i \cdot \mathbb{U}(x_i, x_{i+1}),$$ where $\mathbb{U}(x_i, x_{i+1})$ denotes ...
215 views

### Safety stock for log-normal distribution demand

I came across this example on how to model your lead time demand as a log-normal distribution and calculate the safety stock. https://www.linkedin.com/pulse/why-you-keep-missing-your-service-level-...
222 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 ...
901 views

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 ...