CONTENTS 4.1 Introduction 4.2 Discrete Probability Distributions 4.3 Continuous Probability Distributions 4,4 Conclusion Important Probability Distributions Introduction to Statistics and Econometrics June25,2019 6/135
Important Probability Distributions Introduction to Statistics and Econometrics June 25, 2019 6/135 4.1 Introduction 4.2 Discrete Probability Distributions 4.3 Continuous Probability Distributions 4.4 Conclusion CONTENTS
Important Probability Distributions Discrete Probability Distributions Bernoulli Distribution A DRV X follows a Bernoulli(p)distribution if its PMF x={-p fx=1, if x=0, =p2(1-p)1-for x=0,1, 0.8 where 0<p<1 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 Remark: 0 Bernoulli(0.75) This is a binary random variable,taking value 1 with probability p,and taking value 0 with probability 1-p. Important Probability Distributions Introduction to Statistics and Econometrics June25,2019 7/135
Important Probability Distributions Important Probability Distributions Introduction to Statistics and Econometrics June 25, 2019 7/135 Bernoulli Distribution Discrete Probability Distributions Remark:
Important Probability Distributions Discrete Probability Distributions Bernoulli Distribution Remarks: ●For Bernoulli(p), EX) P, var(X) p(1-p). ●MGF of Bernoulli(p) Mx(t)=pe +1-p for -oo<t<oo. Because p=P(X 1)and X only takes two possible values,parameter p fully characterizes the probability distribution of Bernoulli(p). Important Probability Distributions Introduction to Statistics and Econometrics June25,2019 8/135
Important Probability Distributions Important Probability Distributions Introduction to Statistics and Econometrics June 25, 2019 8/135 Bernoulli Distribution Discrete Probability Distributions Remarks:
Important Probability Distributions Discrete Probability Distributions Bernoulli Distribution Remarks: Bernoulli(p)has wide applications in e economics and finance: Neftci (1984)examines the asymmetry of U.S. business cycles by considering the time series properties of signed processes from a posi- tive change to a negative change,and from a negative change to a positive change. Important Probability Distributions Introduction to Statistics and Econometrics June25,2019 9/135
Important Probability Distributions Important Probability Distributions Introduction to Statistics and Econometrics June 25, 2019 9/135 Bernoulli Distribution Discrete Probability Distributions Remarks:
Important Probability Distributions Discrete Probability Distributions Bernoulli Distribution Remarks: -Das (2002)approximates jumps of interest rates by a sequence of Bernoulli random variables. -Logit regression model P(X=1Z)= 1 1+exp(-B'Z) Important applications of logit regression include pattern recognition and classification analysis. Important Probability Distributions Introduction to Statistics and Econometrics June25,2019 10/135
Important Probability Distributions Important Probability Distributions Introduction to Statistics and Econometrics June 25, 2019 10/135 Bernoulli Distribution Discrete Probability Distributions Remarks: