The SpHere INfrared Exoplanet (SHINE) project is a 500-star survey performed with SPHERE on the Very Large Telescope for the purpose of directly detecting new substellar companions and understanding their formation and early evolution. Here we present an initial statistical analysis for a subsample of 150 stars spanning spectral types from B to M that are representative of the full SHINE sample. Our goal is to constrain the frequency of substellar companions with masses between 1 and 75 M_Jup and semimajor axes between 5 and 300 au. For this purpose, we adopt detection limits as a function of angular separation from the survey data for all stars converted into mass and projected orbital separation using the BEX-COND-hot evolutionary tracks and known distance to each system. Based on the results obtained for each star and on the 13 detections in the sample, we use a Markov chain Monte Carlo tool to compare our observations to two different types of models. The first is a parametric model based on observational constraints, and the second type are numerical models that combine advanced core accretion and gravitational instability planet population synthesis. Using the parametric model, we show that the frequencies of systems with at least one substellar companion are 23.0_−9.7^+13.5, 5.8_−2.8^+4.7, and 12.6_−7.1^+12.9% for BA, FGK, and M stars, respectively. We also demonstrate that a planet-like formation pathway probably dominates the mass range from 1–75 M_Jup for companions around BA stars, while for M dwarfs, brown dwarf binaries dominate detections. In contrast, a combination of binary star-like and planet-like formation is required to best fit the observations for FGK stars. Using our population model and restricting our sample to FGK stars, we derive a frequency of 5.7_−2.8^+3.8%, consistent with predictions from the parametric model. More generally, the frequency values that we derive are in excellent agreement with values obtained in previous studies.