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A new three-parameter statistical distribution is offered for the description of random strength of a brittle material. The distribution allows characterization of a wide range of relations regarding the strength–size effect. Thus, in contrast to the Weibull distribution, the non-linear character between the logarithm of average strength and the logarithm of the specimen size may be described, while retaining the Weibull function as a limiting case. Furthermore, the proposed distribution permits simple evaluation of the necessary statistical parameters by considering all experimental points for different specimen sizes together. Experimental confirmation of the strength distribution is illustrated using experimental data on three types of glass fibres at three gauge lengths each.