This study introduces a new two-parameter mixed Poisson distribution, namely Poisson-Weighted Exponential (P-WE), which is obtained by mixing Poisson distribution with a new class of weighted exponential distribution. The new P-WE distribution provides a more flexible alternative for modelling over dispersed count data compared to Poisson distribution. The estimation procedures of P-WE distribution via method of moments and maximum likelihood are provided. This study also introduces P-WE regression model which can be fitted to over dispersed count data with covariates. The P-WE distribution and P-WE regression model are fitted to two sets of count data.
This study attempts to find the best model to forecast international tourism demand using a series of key macroeconomic variables in ASEAN countries. Generally, we find that generalized Poisson regression model is the best one for estimating long-run international tourism demand. In addition, we find that inflation and real exchange rate have negative relationship with international tourism demand. On the other hand, foreign direct investment and openness of trade have positive relationship with international tourism demand. Cointegration test result shows that there is a long-run relationship between variables.
This study applies a Bivariate Poisson-Lindley (BPL) distribution for modeling dependent and over-dispersed count data. The advantage of using this form of BPL distribution is that the correlation coefficient can be positive, zero or negative, depending on the multiplicative factor parameter. Several properties such as mean, variance and correlation coefficient of the BPL distribution are discussed. A numerical example is given and the BPL distribution is compared to Bivariate Poisson (BP) and Bivariate Negative Binomial (BNB) distributions which also allow the correlation coefficient to be positive, zero or negative. The results show that BPL distribution provides the smallest Akaike Information Criterion (AIC), indicating that the distribution can be used as an alternative for fitting dependent and over-dispersed count data, with either negative or positive correlation.
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