# Confidence Limits

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## Confidence Limits

Confidence limits for an unknown value of the parameter θ, which correspond to the given coefficient of confidence *p*, are the functions θ_{1},(ξ_{1}, ξ_{2} … , ξ_{n}) and θ_{2},(ξ_{1}, ξ_{2} … , ξ_{n}) of the observations ξ_{1}, ξ_{2} … , ξ_{n}such that for any “permissible” probability distribution, the inequalities

θ_{1},(ξ_{1}, ξ_{2} … , ξ_{n}) ≤ θ ≤ θ_{2} θ_{2},(ξ_{1}, ξ_{2} … , ξ_{n})

are realized with a probability of not less than *P* (and, consequently, are violated with a probability of not greater than 1 - *P*).