Up to now, various studies for finding the mutual relationship among several type noise evaluation indices closely connected with an equivalent continuous sound level, L_<eq>, and a widely used evaluation index, L_x. which are very important in the field of noise evaluation and regulation problems, were reported by many investigators. Almost all of these studies, however, were confined only to the practical method of applying directly the well-known linear regression analysis method to actually observed data and/or finding an approximate evaluation under the assumption of a standard Gaussian distribution form of level fluctuations. If one want to find universally and objectively the more precise relationship among the above noise evaluation indices for the non-Gaussian type actual noise level fluctuations in a daily life, one can not use the above practical method just as it is. From such an essential point of view, in this paper, a general theory for the mutual relationship among several type noise evaluatin indices connected with two typical indices, L_<eq> and L_x, which is objectively applicable for any kind of random noise data, has been first proposed in a general form including the well-known simplified relationship based on the Gaussian distribution in a special case. Finally , the validity of the proposed theory has been experimentally confirmed too by applying it to the actually observed road traffic noise
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