There are limited studies on how the distribution of daily rainfall and its extremes has varied across Australia and the globe. Here we present an analysis to systematically analyse the changes in the entire probability density function (PDF) of daily rainfall at each grid cell across Australia. Such an analysis also has the potential to be applied globally. Temporal changes were assessed by comparing quantiles of each station PDF over two periods - 1958 to 1985 and 1986 to 2013. Changes in the interquartile range (IQR) and the Yule-Kendell skewness measure were used to investigate scale and shape changes of the PDFs, and we calculated quantile ratios to assess changes for specific parts of the PDF. Our findings suggest that the number of wet days have decreased particularly in the east coast and the south western tip of Western Australia while the median and IQR have increased across most areas as have the upper quantile extremes. Our findings also suggest that the highest extremes do not scale with the medians and that at various locations across Australia there is a drastic change in the highest extremes.