The prior function to calculate the Beta prior parameters

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`type` |
type of prior information: "MeanVar" uses mean and variance, "Optimist" uses (ORR) mean, "ORRN" uses ORR and smaple size, "ORRW" uses ORR and CI width. |

`mu` |
prior(ORR) mean. |

`v` |
prior variance |

`N` |
prior sample size. |

`W` |
prior confidence interval width. |

`init` |
initial value to solve the nonlinear equations for "ORRW" type. |

`parameters` |
the vector of Beta parameters: |

Thall, P. F., Simon, R. (1994).
Practical Bayesian guidelines for phase IIB clinical trials.
*Biometrics* **50**: 337-349.

Mayo, M. S., & Gajewski, B. J. (2004).
Bayesian sample size calculations in phase II clinical trials using informative conjugate priors.
*Controlled clinical trials* **25**(2): 157-167.

Tan, S. B., & Machin, D. (2002).
Bayesian two-stage designs for phase II clinical trials.
*Statistics in medicine* **21**(14): 1991-2012.
New York: Wiley.

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