Introduction to Probability Models¶
Ross, S. M. (2014). Introduction to Probability Models. Academic Press.
Cited by¶
4 citations across 4 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Funnel Analysis
- It can be modeled as a Markov chain with terminal absorbing states, as a survival process, or as a series of stage-wise Bernoulli trials.
This sourceStandard applied-probability text covering Markov chains with absorbing states, expected time in transient states, and Bernoulli-trial sequences — the formal models for sequential filtering of a population through stages to terminal/absorbing outcomes.
- It can be modeled as a Markov chain with terminal absorbing states, as a survival process, or as a series of stage-wise Bernoulli trials.
- Poisson Process
- Three commitments define it and are equivalent to one another under mild conditions: the number of events in disjoint intervals are independent; the count in any interval of length \(t\) is Poisson-distributed with mean \(\lambda t\); and the waiting times between consecutive events are independent and exponentially distributed with rate \(\lambda\).
This sourceStandard text defining the Poisson process via its three equivalent characterizations (independent increments, Poisson counts, exponential inter-arrivals) and deriving superposition, thinning, the uniform order-statistics property, the inspection paradox, and the law of rare events.
- Three commitments define it and are equivalent to one another under mild conditions: the number of events in disjoint intervals are independent; the count in any interval of length \(t\) is Poisson-distributed with mean \(\lambda t\); and the waiting times between consecutive events are independent and exponentially distributed with rate \(\lambda\).
Domain-specific¶
Mechanisms¶
- Cumulative Risk Horizon Table
- For independent opportunities it fills each cell with the cumulative-occurrence relation `1 − (1 − p)ⁿ`
This sourceFor independent opportunities with probability p, the chance of at least one occurrence in n trials is 1 − (1 − p)^n.
- For independent opportunities it fills each cell with the cumulative-occurrence relation `1 − (1 − p)ⁿ`
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