Welch & Peers (1963) used a root-information prior to obtain posterior PROBABILITIES for a scalar parameter exponential model and showed that these Bayes PROBABILITIES had the confidence property to second order asymptotically. An important undercurrent of this indicates that the constant information reparameterization provides location model structure, for which the confidence property was and is well known. This paper examines the role of the scalar-parameter exponential model for obtaining APPROXIMATE PROBABILITIES and APPROXIMATE confidence levels, and then addresses the extension for the vector-parameter exponential model.

Typographical data entry errors and incomplete documents, produce imperfect records in real world databases. These errors generate distinct records which belong to the same entity. The aim of APPROXIMATE Record Matching is to find multiple records which belong to an entity. In this paper, an algorithm for APPROXIMATE Record Matching is proposed that can be adapted automatically with input error patterns. In field matching phase, edit distance method is used. Naturally, it had been customized for Persian language problems such as similarity of Persian characters, usual typographical errors in Persian, etc. In record matching phase, the importance of each field can be determined by specifying a coefficient related to each field. Coefficient of each field must be dynamically changed, because of changes of typographical error patterns. For this reason, Genetic Algorithm (GA) is used for supervised learning of coefficient values. The simulation results show the high abilities of this algorithm compared with other methods (such as Decision Trees).

In the excess loss reinsurance risk model, the amount of insurance premium paid by the company is influential in the ruin of that company. In this paper, the premium function is presented based on the expected amount of total payments of the reinsurer to the assigning insurer, the constraint on this function is investigated, and for the claims with any arbitrary distribution, the contour plots are drawn and with presenting optimization algorithm, infinite time ruin probability function will be minimum for different values of initial capital and threshold value. Finally, the excess loss reinsurance risk model with non-exponential claims is considered, and the infinite time ruin probability is calculated with numerical examples.

In this paper, we prove that every orthogonally higher ring derivation is a higher ring derivation. Also we find the general solution of the pexider orthogonally higher ring derivations {fn(x + y) = gn(x) + hn(y), = 0, {fn(xy) =∑, i+j=n gi (x)hj (y). Then we prove that for any APPROXIMATE pexider orthogonally higher ring derivation under some control functions φ, (x, y) and ψ, (x, y), there exists a unique higher ring derivation D = {dn}∞,n=0, near {fn}∞,n=0, {gn}∞,n=0 and {hn}∞,n=0 estimated by φ,and ψ, .