Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [interarrival-time]

The time between the arrival of one point & the next, as in a point process or queue. More abstractly, 'time' can be a distance between 2 points in a space.

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Distribution to reflect situation where some waiting leads us to expect more waiting

In reading Blake Master's notes on Peter Thiel's lecture on start ups, I came across this metaphor of the technology frontier: Picture the world as being covered by ponds, lakes, and oceans. You’re in a boat, in a body of water. But it’s…
Andy McKenzie
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Number of events in a segment if waiting times are drawn from a mixture of two exponential distributions

What is the probability for $n$ events to occur over a period of time $t$, if the duration of each event is a random variable distributed as a mixture of two exponential distributions, one with the average duration $\tau_1$ and the probability $p$…
golobor
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Finite state machine with gamma distributed waiting times

I have a state machine with positive and negative inputs. The time between positive inputs follows a gamma distribution ($X_+ \sim \Gamma(k_+, \theta_+)$), and the time between negative inputs follows a different gamma distribution ($X_- \sim…
mwoods
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What is the difference between the Poisson distribution and the uniform distribution?

I'm modeling a factory with orders arriving independently of each other. I need a series of actual time stamps of arrivals. I've been told that everyone uses the Poisson distribution to model arrivals. Fine. But what I can't understand is how…
user7392
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Estimating Poisson process intensity using GLM

Suppose I want to build an explanatory model for events generated by an inhomogeneous Poisson process with unknown intensity $\lambda$. Each entry in my dataset represents the registration of an event: time $t_i$, location $(x_i,y_i)$ and some…
seneca
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Non-parametric (smoothed) estimate of current rate

I am looking at time-series event data and need to visualize how the arrival rate $\lambda$ changes over time. I do not want to assume any underlying distribution that the data comes from (it is certainly not a Poisson process as the rate changes,…
eithompson
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two independent Poisson Arrivals

I have two types of customers (type 1 and type 2) enter a shop. Their arrival processes are independent and follow Poisson process with the arrival rates of $\lambda_1$ and $\lambda_2.$ Consider two events where $A = \{\text{customer } q+1 \text{ is…
Ebi1990
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Minimum interval such that $X\%$ of intervals will contain $\ge Y$ events

I have a data set that contains the dates and times of purchases. Say I have one month of data for the purchases. I am looking for the interval of time, say 10 mins / 30 mins / hourly, for which 90% of such intervals will contain at least a…
ac927
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Conditional distribution of arrival times in Poisson process

Suppose I know over a window $[0, T)$ that I have observed $n$ samples from a poisson process $N_t \sim p(n|\lambda t) = \frac{1}{n!}(\lambda t)^{n}\exp(-\lambda t)$. What is the conditional distribution of the arrival times $t_1 < t_2 < ... <…
user27886
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For binomial success / fail data, how to calculate if the time since last success is out of the normal range

Struggling to figure this out. I have data sets that are essentially ObjectId, Date, Pass/Fail (1/0) The data is normally daily. What I want to figure out is IF the number of days since the last pass is normal, or, out of the ordinary For some of…
Eric
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Example of dataset where the data collected at time-points $g(t_1), g(t_2), \ldots$

What would be some practical scenarios where we collect data at time-points $g(t_1), \ldots, g(t_n)$, where $g$ is an increasing function? For example, $g(t) = \exp(t)$ or $\ln t$. To be more clear, in which real-life scenarios we consider dataset…
Joy
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Poisson process and queuing system

In a queuing system, the inter-arrival times are known to be exponentially distributed. My textbook states: "It can be shown that, if the underlying distribution of inter-arrival times { T1, T2, ..., Tn } is exponential, the arrival times are…
Akshit Bhalla
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Interarrival times of exponential distribution

I would like to find the pdf for the $n-1$ interarrival times $w$ of $n$ iid events from an exponential distribution of time constant $\tau$. Using the fact that the first event follows an exponential distribution of time constant $\tau/n$, and…
Mister Mak
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What distributions are possible for an arrival rate?

I'm really struggling to find a good statistical distribution. I've tried Poisson and Gamma so far, but without success (best I've got was a p-value of 0,00005 with a Pearson Chi-Square test). So I really hope you can send me in the right…
Stefan Hessels
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Interarrival time distribution of uniform arrival process

I am currently trying to model an uniform arrival process within my simulation model. However, I can only model it by means of an interarrival time (I can let the model wait for a certain amount seconds). I want to have: $$G(x) = {1 \over…
user32556
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