A random variable that is defined as the absorption time of a finite-state Markov chain is said to have a phase-type (or simply PH) distribution. When the Markov chain is continuous-time, the distribution is continuous and for the discrete-time Markov chains it will be a discrete phase-type distribution. In this thesis we will focus on the continuous phase-type one. The distribution and density functions of a PH distribution can be expressed in terms of ( ? , T ) where ? is the initial state probability distribution and $ T $ is the infinitesimal generator corresponding to the transient states of the Markov chain. The pair ( ?, T ) is known as a representation of the PH distribution. The dimension of T is said to be the order of the representation. Typically representations are non-unique and there must exist at least one representation of minimal order. Such a representation is known as minimal representation, and the order of the PH distribution itself is defined to be the order of any of its minimal representations. The distribution function of a phase-type distribution can be expressed in terms of this representation. This thesis is concerned with the statistical inference for phase-type distributions .The main aim of it is to estimate the parameters ? and T . Under certain regularity conditions, the maximum likelihood estimator (MLE) is a good point estimator, possessing some of the optimality properties: consistency, efficiency, and asymptotic normality. The thesis is focused on finding maximum likelihood estimators of phase-type distributions for continuous case. The Expectation-Maximization (EM) algorithm and Newton-Raphson (NR) method are applied for this purpose. Fisher information has applications in fi nding the variance of an estimator, as well as in the asymptotic behavior of maximum likelihood estimates. This thesis discussed on an explicit formula for computing the observed Fisher information matrix for continuous phase-type distributions, which is needed to estimate the Fisher information matrix . Recent applications of phase-type distributions in stochastic modelling is in areas like queueing theory, reliability theory, renewal theory and survival analysis. This thesis uses the phase-type distribution with the details mentioned. Finally, we present the results of an estimation study considering simulated data from phase–type distributions and use PH distributions to model real data.