Finding a simple probability distribution for human mobile speed

The speed of human mobility in a day is commonly known to have a representative probability distribution and previous studies have identified several useful distributions to represent it. In this study, we deduce conditions for a simple probability distribution that estimates the speed of everyday human mobile with a resolution of 0.01 m/s. A large amount of positioning data was collected using various portable and mobile devices to calculate the speed of human mobility. Considering a range of speeds up to 108 km/h, 180 km/h, 252 km/h, and 360 km/h, several probability distribution functions were deduced in order to establish a base for human mobility research. Our research was conducted using 0.5 m/s, 0.1 m/s, and 0.01 m/s as speed units, because it is possible that smaller units may be meaningful. With permutations of speed ranges and speed units, we extracted probability distributions for human speed and assumed the simplest distribution for actual motion; further, we listed the parameters and conditions for these distributions. Our experimental results indicate that exponential distribution was one of the simplest probability distribution to represent everyday human mobility speeds if a specific speed range is considered and the speed ranges in which the human motion speed follows an exponential distribution was also deduced.