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Questions tagged [poisson-process]

For questions about the theory or applications of the Poisson process, one of the most widely applied point processes in statistics and elsewhere.

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16 views

Multivariate Bayesian Car Model Result

I have developed a multivariate Bayesian Car model for three crash severity level analysis. I found that the covariance for both heterogenous effects and the spatial effect is not significant for any ...
56 views

Confidence interval over multiple Poisson distributions

There are five different periods (one following each other) of unequal lengths where one specific event is happening such that it follows Poisson distributions (e.g. meteorite falls). It is always the ...
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Which distribution or process should be used for wearout reliability modeling?

When modeling the reliability of a system, it is usual to use exponential distribution to model errors that occur randomly throughout the system's useful lifetime (the middle part of the well-known ...
25 views

Extension of Poisson Parameter for Different Temporal Interval

Suppose $Y$ follows a Poisson distribution with parameter $\lambda$ that explains a temporal Poisson process over an interval of 30 seconds. Now, it stands to reason that for an interval of 60 ...
14 views

Test and CI for unstable Poisson process

I have empirical data on a process that I assume is Poisson with a given mean, say $\mu$ (unknown). The data is of the form $(x_i, 1\leq i\leq n)$ for $n$ consecutive time periods. I am concerned ...
57 views

Upper confidence bound for Poisson process rate parameter

I am interested in computing an upper confidence bound for the rate parameter, $\lambda$, in a Poisson process. Specifically, I have a set of observations  X_\text{obs} = \{(n_1,t_1), \ldots, (n_N,...
87 views

Alternating between two states {A, B} each with exp distributed durations. What's the probability of state=A at time t?

Say I have a light bulb that can be on (A) or off (B). It alternates between being state A or B. It will be in state A for a duration a ~ exp(α), and in state B for duration b ~ exp(β), (...
141 views

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 ...
20 views

Poisson Process With Two Different Rates

I am looking to investigate a Poisson Process that has two separate rates; essentially, there is a season of games that each have their own points rate (per minute). Comprehensively, over the season, ...
16 views

Overdispersion under different longitudinal constraints

I have panel data (police districts observed across many months) and I am modeling a count outcome. Fitting a Poisson model (simple pre/post comparison with 6 months of data) results in significantly ...
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How to compute the expected number of events in the following conditional renewal process?

I have a stochastic point process with event times $\{x_1, x_2, ...\}$ and I want to compute the expected number of events $n(T)$ over the interval $[0,T]$. The point process is generated as follows: ...
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How to show the inter-arrival time variance of a Cox process driven by a stationary Poisson process of constant intensity $\lambda$ is $3\lambda$

Ideas on how to show that the variance of a doubly-stochastic Poisson process(aka a Cox process) driven by a homogeneous(stationary) Poisson process of intensity $\lambda$ is $3\lambda$ ? I've come ...
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To detect which of the three processes more-aptly fits Poisson process

There happens to be a type of generic poll, which can be described as:- A participant can vote only once and for only 1 of 3 running candidates - Red, Blue and Green. A random voter starts the ...
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Solving an equation with logarithms of negative numbers

I'm modelling a bunch of non-homogeneous poisson processes. I'm impossing on them a linear-log functional form. you end up with two parameters, theta1 and theta0 for each estimated process. The ...
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Correcting data using poisson-regression

I'm new to stats and I was wondering if anyone had any good resources that could explain to me: How one can correct their data (false-positives) using Poisson-regression. I've been looking for some ...
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How to model arrival times in discrete event simulation where arrivals vary with time of day and day of week

I'm looking for suggestions on how to model inter-arrival times in a discrete event simulation where the arrival rate is highly dependent on the day of week and the hour of day. For example: A ...