In real life situations we can use the information from the past sample to predict the observations of a future sample from the same population with a specified probability. From this procedure we can find intervals with a certain level of significance contain the future predicted values, these intervals are called prediction intervals. Therefore the main subject of this book is the Bayesian prediction intervals (BPI), it is studied using some continuous distributions and nonhomogeneous poisson processes (NHPP).In this book the one sample prediction which predict the future observation from the same sample, and the two sample prediction that use the first sample to predict the future observations, mean, median , range and midrange of the second sample are studied based on ordinary order statistics or generalized order statistics. Besides to BPI, estimation is studied about the exponential distribution with change point and about (NHPP). Prediction is very important in a practical life, for instance medicine, biology, agriculture, business, engineering, industry and quality control.