The characterisation of probability distribution plays an important role in statistical studies. There are various methods of characterisation available in the literature. The characterisation using truncated moments limits the observations; hence, researchers may save time and cost. In this paper, the characterisation of three general forms of continuous distributions based on doubly truncated moments has been studied. The results are given simply and explicitly. Further, the results have been applied to some well-known continuous distributions.
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Species – area (SAR) and species time (STR) relationships describe the increase of species richness with study area and study time and have received much attention among ecologists and are used in different branches of biodiversity research. Unknown sample size effects often hinder a direct comparison of SAR and STR shapes of different taxa and regions. Further, space and time interact during the accumulation of species due to the common sample universe. Here we develop a simple power function scaling model of species richness that integrates space, time, sample size and their interactions. We show that this model is able to precisely describe average species densities and the increase of species richness in a regional metacommunity of a large sample of spiders on Mazurian lake islands (Northern Poland). The model predicts strong area – sample size and time – sample size interactions. Judged from the SAR (z = 0.08) and STR (y = 0.64) slopes it points to only moderate spatial β–diversities but high local temporal species turnover. We suspect that the parameters of many published SARs are strongly influenced by unknown sampling time and sample size effects that make direct comparison difficult.
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