Providing safe travel from one point to another is the main objective of any public transportation agency. The recent publication of the Highway Safety Manual (HSM) has resulted in an increasing emphasis on the safety performance of specific roadway facilities. The HSM provides tools such as crash prediction models that can be used to make informed decisions. The manual is a good starting point for transportation agencies interested in improving roadway safety in their states. However, the models published in the manual need calibration to account for the local driver behavior and jurisdictional changes. The method provided in the HSM for calibrating crash prediction models is not scientific and has been proved inefficient by several studies. To overcome this limitation this study proposes two alternatives. Firstly, a new method is proposed for calibrating the crash prediction models using negative binomial regression. Secondly, this study investigates new forms of state-specific Safety Performance Function SPFs using negative binomial techniques. The HSM's 1st edition provides a multiplier applied to the univariate crash prediction models to estimate the expected number of crashes for different crash severities. It does not consider the distinct effect unobserved heterogeneity might have on crash severities. To address this limitation, this study developed a multivariate extension of the Conway Maxwell Poisson distribution for predicting crashes. This study gives the statistical properties and the parameter estimation algorithm for the distribution. The last part of this dissertation extends the use of Highway Safety Manual by developing a multivariate crash prediction model for the bridge section of the roads. The study then compares the performance of the newly proposed multivariate Conway Maxwell Poisson (MVCMP) model with the multivariate Poisson Lognormal, univariate Conway Maxwell Poisson (UCMP) and univariate Poisson Lognormal model for different crash severities. This example will help transportation researchers in applying the model correctly.