A state probability measures the likelihood that a process occupies a particular state during a specified period. In Markov analysis, states must be collectively exhaustive and mutually exclusive, so each system instance belongs to exactly one state. section 11.2
Represent the probabilities as a vector π = (π₁, π₂, …, πₙ), where πᵢ is the probability of occupying state i. The entries sum to 1, and periods must use consistent units such as days, weeks, quarters, or years. section 11.2 section 11.2.1
Use state probabilities to:
- Describe the initial distribution of a system before transitions occur. section 11.2
- Combine current state probabilities with transition probabilities to forecast how a distribution changes over time. section 11.2.1
- Translate market shares into probabilities when each consumer belongs to one carrier state. section 11.2.1
Four-carrier market distribution
Assign Horizon 0.40, TeleConnect 0.35, AmeriCon 0.20, and USAMobile 0.05. The vector (0.40, 0.35, 0.20, 0.05) describes the probability that a randomly selected consumer subscribes to each carrier in period 0; its entries sum to 1. section 11.2.1
