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This paper presents a method for transformer loss-of-life inference by integrating stochastic dependence between non-normal transformer load and ambient temperature into analysis. The non-normally distributed variables are transformed to a common domain (i.e., the rank domain) by applying the cumulative density function transformation. In this domain, special functions, copulas, are used for modeling stochastic dependence between the variables. Extensive research data have been used to obtain quantitative results for realistic test cases of distribution transformers serving various types of low-voltage consumers. The results indicate that the accuracy of loss-of-life inference is very sensitive to normality and independence assumptions which are generally adopted in previous studies. It is demonstrated that such assumptions may lead to misleading results compared to the actual conditions. Thus, the proposed method, which is based on no restrictive assumption, emerges as a more accurate solution for transformer loss-of-life inference.