dpoisBCD | R Documentation |
Computes the joint probability mass function (p.m.f.) of a Bivariate Poisson Conditionals distribution (BPCD) based on Ghosh, Marques, and Chakraborty (2021).
dpoisBCD(x, y, lambda1, lambda2, lambda3)
x |
value of |
y |
value of |
lambda1 |
rate parameter for |
lambda2 |
rate parameter for |
lambda3 |
dependence parameter that must be |
The joint p.m.f. of the BGCD is
P(X = x, Y = y) = K(\lambda_1, \lambda_2, \lambda_3) \frac{\lambda_1^x \lambda_2^y \lambda_3^{xy}}{x! y!},
where x, y = 0, 1, 2, \ldots
, and K(\lambda_1, \lambda_2, \lambda_3)
is the normalizing constant computed by the function normalize_constant_BPCD
.
Key properties of the BPCD include:
- Negative correlation for \lambda_3 < 1
,
- Independence for \lambda_3 = 1
.
probability P(X = x, Y = y)
for each pair of x
and y
.
Ghosh, I., Marques, F., & Chakraborty, S. (2021). A new bivariate Poisson distribution via conditional specification: properties and applications. Journal of Applied Statistics, 48(16), 3025-3047. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/02664763.2020.1793307")}
rpoisBCD
, ppoisBCD
# Compute P(X = 1, Y = 2) with lambda1 = 0.5, lambda2 = 0.5, lambda3 = 0.5
dpoisBCD(x = 1, y = 2, lambda1 = 0.5, lambda2 = 0.5, lambda3 = 0.5)
# Compute P(X = 0, Y = 1) with lambda1 = 0.5, lambda2 = 0.5, lambda3 = 0.5
dpoisBCD(x = 0, y = 1, lambda1 = 0.5, lambda2 = 0.5, lambda3 = 0.5)
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