Hypergeometric functions of matrix arguments occur frequently in multivariate statistical analysis. In this paper, we define and study extended forms of Gauss and confluent hypergeometric functions of matrix arguments and show that they occur naturally in statistical distribution theory.

Rainfall is one of the most predominant geophonic sources in nature, and the major climatic phenomenon influencing species biology in tropical ecosystems. Although its effects on acoustic indices have been studied, rainfall is recognized as a nuisance factor affecting their estimation. Consequently, files with rainfall sounds are typically removed from ecoacoustic analyses. In tropical rainforests, where rainfall is a common and unpredictable event, its influence on acoustic indices needs to be explicitly examined before implementing acoustic passive monitoring. Using mixed‐effects models we assessed the effect of different rainfall conditions on the direction and magnitude of the values of eight commonly used acoustic indices. We obtained 18336 1‐min recordings from 28 sampling sites in a montane forest on the northern Andes of Colombia between May‐July 2018. We identified 2867 1‐min recordings containing light to heavy rainfall. We found that both rainfall occurrence and its variation in intensity were associated with increases in ACI, ADI, H, and M index values, and decreases in AEI, BI, NDSI, and NP values. The estimated indices exhibited differential sensitivity to rainfall, with M, NDSI, and NP showing higher differences associated with increasing frequency and intensity of rainfall. Regardless the direction of change in index values caused by rainfall, we found that the magnitude of variation depended on the index. For instance, ACI and BI indices showed low sensitivity and can be considered as reliable acoustic metrics, even during heavy intensity rainfall. In contrast, M, NDSI, and NP might lead to misleading inferences, if rainfall events are not considered during calculation. We stress the importance of careful interpretation of biological inferences based on these sensitive indices and encourage an explicit assessment of rainfall, particularly in short‐term acoustic surveys in highly pluvious regions where rainfall is a conspicuous component of the soundscape.

In this article, we study several properties of extended Gauss hypergeometric and extended confluent hypergeometric functions. We derive several integrals, inequalities and establish relationship between these and other special functions. We also show that these functions occur naturally instatistical distribution theory.