Is the poisson distribution a useful tool in statistics in the tourism sector? In the business world there is a lot of information that results from the activities and tasks performed daily according to the heading and line of business. This important information is often not taken into account for an analysis that allows making the best decisions. However, this information should be well used to estimate similar future scenarios and respond in the best way to similar situations, to avoid falling into sometimes serious errors. Well, for this, there are statistics, a science that collects, organizes, presents, analyzes and interprets data in order to promote more effective decision-making (Lind, Marchal and Wathen; 2012). In the tourism sector, a varied sector,where the hotel industry and the gastronomic industry are included, it has been growing year after year in Peru, it has information on the tourist activities that have been carried out in the interior and outside the country, and can be well used by all entities and public institutions and private for better decision making. Likewise, the statistics and information of these activities are related to time, distance or area, such as, for example: the number of tourist arrivals to Peru in a given year, the number of tourists in Machu Picchu, the delay time of travel from city to city, the distance between Lima and Cusco, the number of rooms occupied by national tourists, the percentage of restaurants occupied in national holidays, etc. Under these parameters,This essay will detail the concepts of the Poisson Discrete Probability Distribution, comparing it with other discrete probability distributions, and its application in the tourism sector for better decision making.
As has been well mentioned, tourism is an area where various activities are carried out where there is a lot of information and useful statistics for good decision making. To make good decision-making, scenarios with favorable probability results must be proposed, so this statistical information is of a discrete nature, that is, it adopts a number of separate values, such as, for example: 5 days of travel in On average, 3,500,000 tourists visited Peru this year, 650 dollars is the average expenditure per tourist in their visit to Lima, among other data. That is why the best tool for defining probabilities is the discrete probability distribution.
Within the discrete probability distributions, the best known and most used are the Binomial, Poisson and Hypergeometric distribution. The first presents two favorable results: success or failure and its probability is the same in each trial. It also contains a fixed number of trials independent of each other. In the case of Poisson, it adds a defined interval of time (area, distance, time or other unit of measure) and independent, and the probability of the event happening is proportional to the size of the interval. Finally, the Hypergeometric distribution presents the results of each trial in success or failure and the trials are not independent. Also, samples are run with a finite population without replacement, and the probability of success changes with each trial.
As is known, all these distributions measure an exact probability and in the case of tourism there is one of them that has the best possible application. This is the poisson distribution, which has the characteristic of measuring the probability as a function of a number of individuals per unit of time, space, distance, area, it is applicable in any similar unit of measurement as stated by Triola (2004). According to Gestiopolis (2016), the poisson distribution is a discrete variable distribution in which its main applications refer to the modeling of situations in which we are interested in determining the number of events of a certain type that can occur in a interval of time or space. Likewise, Kazmier (1991) mentions that this distribution occurs in a continuum,instead of occurring in trials or fixed observations. The distribution is based on two assumptions: the probability is proportional to the length of the interval, that means that the larger the interval, the greater the probability and the intervals are independent. This distribution supports the so-called binomial distribution when there is a very small probability of success and a large sample size, or else when the sample size is greater than 30.This distribution supports the so-called binomial distribution when there is a very small probability of success and a large sample size, or else when the sample size is greater than 30.This distribution supports the so-called binomial distribution when there is a very small probability of success and a large sample size, or else when the sample size is greater than 30.
In this way, Poisson distribution is applied in the tourism business and its various industries such as: visitor accommodation (including hotels and similar establishments), food and beverage provision activities (mainly restaurants), passenger transport (by rail, by road, by water and air), activities of travel agencies and other reservation services and other tourism industries. The main entity worldwide that provides statistics related to the tourism sector is the World Tourism Organization, which publishes annually a Compendium of Tourism Statistics (2014) that shows statistical indicators of inbound tourism, outbound tourism, domestic tourism, tourism employment, complementary macroeconomic indicators, among others.These indicators should be used by companies that wish to promote tourism under a complete statistical analysis, with the use of statistical tools, such as the Poisson Distribution.
For example, national tourists make 4 trips to the interior of the country each year. In this case, travel agencies can design their tourist packages based on the number of annual visits they make to the interior of the country. Well, in this way, the travel agency can define the probability that one, two, three, four or more annual visits are made, under the assumptions of the poisson distribution. Thus, the mean number of trips to the interior of the country is 4, and the probability that 0 trips are made is 2%; 1 trip, 7%; 2 trips, 15%, 3 trips, 20%, 4 trips, 20% and more than 4 trips is 37%. Now, making another assumption in which a hotel entrepreneur wants to open a hotel in La Libertad, he will need statistics on the number of overnight stays per person between the months of December and April mainly. So that,According to the Profile of the National Vacationer who visits La Libertad by PROMPERU (2014), it shows that the nights spent by each person in La Libertad is on average 6. Also, applying the poisson distribution, the probability that a person stays overnight is 0 2 nights at the hotel is 7%; from 3 to 5 nights, 38% and more than 6 nights, 55%. With these probabilities, you will make the most accurate decision whether or not to open a hotel.
Likewise, in the gastronomic industry, there are luxury restaurants where an average of 5 customers per hour are received between 12pm and 4pm. The restaurant owner knows that, on average, 5 customers arrive at that time and for which he wants to know the probability that more than 5 customers will arrive. For this case, the average number of diners visit is 5 times the average number of customers who arrive between 12pm and 4pm and the probability that 5 people will finally arrive is 38.4%. Likewise, it is advisable to determine the probability that 0 to 1 customer will arrive, 4%; from 2 to 3 clients, 22% and from 4 to 5 clients, 35%. In this way, the owner can estimate the amount of dishes for his clientele.
On the other hand, an assumption can be made considering the average annual expenditure of foreign tourists in our country. For which, the Ministry of Foreign Trade and Tourism may consider the probability that in the next year it will spend an equal or greater amount to estimate the foreign exchange that these visits could generate. According to PROMPERU (2014), the average spending in 2014 was US $ 992, and the probability that they will spend up to US $ 1,000 on their next trip is 60.8% and more than US $ 1,000 is 39.2%. This concludes that, in the next year, it is very likely that an average of US $ 992 will continue to be spent.
As can be seen, the poisson distribution is a useful and exact tool in determining probabilities in situations of tourist activities such as those seen above. This distribution is relevant, because it not only considers aspects of time, but also space and place, key factors in the tourism industry. With this, managers, directors and people responsible for their companies or public entities will have greater certainty in making decisions strategically and avoid falling into the same mistakes.
References
- Gestiopolis (2016). What is the Poisson distribution? Retrieved March 25, 2016, from http://www.gestiopolis.com/que–es–la–distribucion–de–poisson/ Kazmier (1991). Probability distributions for discrete random variables: binomial, hypergeometric and poisson. In Statistics applied to administration and economics (pp. 103 - 125). Mexico DF: McGraw - Hill.Lind, D., Marchal, W. and Wathen, S. (2012) Statistics Applied to Business and the Economy. McGraw Hill Ed. 15.PROMPERU (2014). Profile of the National Vacationer 2014. Retrieved on March 25, 2015, from: http://media.peru.info/IMPP/2014/Perfil–National Vacationer / Place – Visited / PVN – 2014 – Vacationers – who – visited – The –Libertad.pdfPROMPERU (2014). Profile of the Foreign Tourist 2014. Retrieved on March 26, 2015, from: http://media.peru.info/IMPP/2014/Perfil–Turista–Extranjero/Perfil–del– Turista – Extranjero – 2014 – Consolidado.xlsx PROMPERU (2012). Arrivals at the Lodging Establishments - Ayacucho. Retrieved March 26, 2015, from: http://intranet.promperu.gob.pe/IMPP/2010/EstadisticasPeru/Arribos%20a%20los%20E stablelaciones% 20de% 20Hospedaje / Ayacucho.xls Triola (2004). Probability distributions. In Statistics (pp. 180-223). Mexico DF.: Pearson EducationWorld Tourism Organization (2014). Compendium of tourism statistics. Retrieved March 25, 2016; from: http://statistics.unwto.org/es/content/compendio–de–estadisticas–de–turismo
