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A simple statistical model of daily precipitation based on the gamma distribution is applied to summer (JJA in Northern Hemisphere, DJF in Southern Hemisphere) data from eight countries: Canada, the United States, Mexico, the former Soviet Union, China, Australia, Norway, and Poland. These constitute more than 40% of the global land mass, and more than 80% of the extratropical land area. It is shown that the shape parameter of this distribution remains relatively stable, while the scale parameter is most variable spatially and temporally. This implies that the changes in mean monthly precipitation totals tend to have the most influence on the heavy precipitation rates in these countries. Observations show that in each country under consideration (except China), mean summer precipitation has increased by at least 5% in the past century. In the USA, Norway, and Australia the frequency of summer precipitation events has also increased, but there is little evidence of such increases in any of the countries considered during the past fifty years. A scenario is considered, whereby mean summer precipitation increases by 5% with no change in the number of days with precipitation or the shape parameter. When applied in the statistical model, the probability of daily precipitation exceeding 25.4 mm (1 inch) in northern countries (Canada, Norway, Russia, and Poland) or 50.8 mm (2 inches) in mid-latitude countries (the USA, Mexico, China, and Australia) increases by about 20% (nearly four times the increase in mean). The contribution of heavy rains (above these thresholds) to the total 5% increase of precipitation is disproportionally high (up to 50%), while heavy rain usually constitutes a significantly smaller fraction of the precipitation events and totals in extratropical regions (but up to 40% in the tropics, eg., in southern Mexico). Scenarios with moderate changes in the number of days with precipitation coupled with changes in the scale parameter were also investigated and found to produce smaller increases in heavy rainfall but still support the above conclusions. These scenarios give changes in heavy rainfall which are comparable to those observed and are consistent with the greenhouse-gas-induced increases in heavy precipitation simulated by some climate models for the next century. In regions with adequate data coverage such as the eastern two-thirds of contiguous United States, Norway, eastern Australia, and the European part of the former USSR, the statistical model helps to explain the disproportionate high changes in heavy precipitation which have been observed.