Оқиғаның қайталану мерзімі: Статистикалық талдау

Estimated recurrence time of an eventthe satellite return period

A return period, also known as a recurrence interval or repeat interval, is an average time or an estimated average time between events such as earthquakes, floods, landslides, or river discharge flows to occur. It is a statistical measurement typically based on historic data over an extended period, and is used usually for risk analysis. Examples include deciding whether a project should be allowed to go forward in a zone of a certain risk or designing structures to withstand events with a certain return period. The following analysis assumes that the probability of the event occurring does not vary over time and is independent of past events.

The theoretical return period between occurrences is the inverse of the average frequency of occurrence. For example, a 10 year flood has a 1/10 = 0.1 or 10% chance of being exceeded in any one year and a 50 year flood has a 0.02 or 2% chance of being exceeded in any one year. This does not mean that a 100 year flood will happen regularly every 100 years, or only once in 100 years. Despite the connotations of the name "return period". In any given 100 year period, a 100 year event may occur once, twice, more, or not at all, and each outcome has a probability that can be computed as below. Also, the estimated return period below is a statistic: it is computed from a set of data (the observations), as distinct from the theoretical value in an idealized distribution. One does not actually know that a certain or greater magnitude happens with 1% probability, only that it has been observed exactly once in 100 years. That distinction is significant because there are few observations of rare events: for instance if observations go back 400 years, the most extreme event (a 400 year event by the statistical definition) may later be classed, on longer observation, as a 200 year event (if a comparable event immediately occurs) or a 500 year event (if no comparable event occurs for a further 100 years). Further, one cannot determine the size of a 1000 year event based on such records alone but instead must use a statistical model to predict the magnitude of such an (unobserved) event. Even if the historic return interval is a lot less than 1000 years, if there are a number of less severe events of a similar nature recorded, the use of such a model is likely to provide useful information to help estimate the future return interval.

One would like to be able to interpret the return period in probabilistic models. The most logical interpretation for this is to take the return period as the counting rate in a Poisson distribution since it is the expectation value of the rate of occurrences. An alternative interpretation is to take it as the probability for a yearly Bernoulli trial in the binomial distribution. That is disfavoured because each year does not represent an independent Bernoulli trial but is an arbitrary measure of time. This question is mainly academic as the results obtained will be similar under both the Poisson and binomial interpretations.