Show Distribusi Poisson adalah distribusi yang menunjukkan kemungkinan berapa kali suatu peristiwa akan terjadi dalam periode waktu yang ditentukan sebelumnya. Ini digunakan untuk peristiwa independen yang terjadi pada kecepatan konstan dalam interval waktu tertentu. Distribusi Poisson merupakan fungsi diskrit, artinya peristiwa hanya dapat diukur sebagai terjadi atau tidak terjadi, artinya variabel hanya dapat diukur dalam bilangan bulat. Kami menggunakan pustaka python seaborn yang memiliki fungsi bawaan untuk membuat grafik distribusi probabilitas seperti itu. Juga paket scipy membantu menciptakan distribusi binomial. from scipy.stats import poisson import seaborn as sb data_binom = poisson.rvs(mu=4, size=10000) ax = sb.distplot(data_binom, kde=True, color='green', hist_kws={"linewidth": 25,'alpha':1}) ax.set(xlabel='Poisson', ylabel='Frequency') Its keluaran adalah sebagai berikut - Ini adalah tutorial mendetail tentang Distribusi NumPy Poisson. Pelajari cara menerapkan Distribusi Poisson di NumPy dan visualisasikan menggunakan Seaborn. Distribusi ini adalah distribusi diskrit di mana kami memiliki kumpulan data diskrit. Data ini tidak dalam bentuk data kontinu. Dalam tipe data ini,
kami memiliki tipe tertentu dari nilai yang ditentukan, dan hasilnya tidak boleh melebihi nilai-nilai ini. Distribusi ini membantu kita dalam menghitung probabilitas terjadinya suatu peristiwa. Peristiwa ini akan berlangsung pada waktu tertentu yang ditentukan. Hasilnya, kita mengetahui tentang terjadinya suatu peristiwa dan berapa kali peristiwa itu akan terjadi. Juga, peristiwa itu terjadi dalam jangka waktu tertentu, bukan sebelum atau sesudah waktu itu. Distribusi ini mengambil dua parameter ini sebagai input: Mari Anda berikan contoh untuk memahaminya dengan lebih baik: Keluaran: Di sini, dalam contoh ini, kami telah memberikan tingkat kemunculan sebagai empat dan bentuk array sebagai lima. Hasilnya, kita mendapatkan hasil berikut. Dalam distribusi normal, kami memiliki data kontinu, sedangkan dua distribusi lainnya memiliki binomial dan Poisson
memiliki kumpulan data diskrit. Mereka dapat menjadi serupa ketika standar deviasi dan mean tertentu dapat cocok dan juga ver besar, dan p mendekati nol sangat identik dengan distribusi Poisson karena n*p sama dengan lam. #pemrograman #python #numpy wtmatter.comIni adalah tutorial mendetail tentang Distribusi NumPy Poisson. Pelajari cara menerapkan Distribusi Poisson di NumPy dan visualisasikan menggunakan Seaborn. The Poisson distribution in RR has several built-in functions for the Poisson distribution. They’re listed in a table below along with brief descriptions of what each one does. Table of Contents
We will begin our demom with
This single observation isn’t very interesting on its own because there’s nothing we can say about it that hasn’t already been said. The first somewhat interesting thing we’ll do with
Predicting the number of babies born in a hospitalThe following question was taken from Probability in with Applications in R by Robert Dobrow. Data from the maternity ward in a certain hospital shows that there is a historical average of 4.5 babies born in this hospital every day. What is the probability that 6 babies will be born in this hospital tomorrow? First, let’s calculate the
theoretical probability of this event using
The theoretical probability of 6 babies being born tomorrow if the historical average is 4.5 is about 13%. Now let’s try simulating births in this hospital for a year (
The simulated result of about 11.5% is pretty close to our theoretical probability of about 13%. What about the probability of more than 6 babies being born?
This theoretical
probability is about 16.9%. Remember that cumulative probability functions in R calculate P(X > x) when What about the corresponding proportion in our simulation?
The simulated proportion of about 18.6% is pretty close to the theoretical proportion we calculated above. Simulating deaths by horse kick of Prussian cavalry soldiersThe data for this simulation comes from Probability in with Applications in R by Robert Dobrow. One of the most famous studies based on the Poisson distribution was by Ladislaus Bortkiewicz, a Polish economist and statistician, in his book The Law of Small Numbers. This book actually contained two studies: one about deaths by horse kicks of Prussian cavalry soldiers and one about child suicides in Prussia. The former is far better known than the latter, probably because its topic is far less grim. The results of his horse kicking death study are still used to teach students about the Poisson distribution today, and our class will be no exception. In his study, Bortkiewicz considered 20 years of data for 10 corps (groups) of Prussian cavalry soldiers. Over this period there were 122 total deaths by
horse kick among these soldiers. Bortkiewicz divided the data into 20 individual periods for each group of soldiers, for a total of 20 x 10 = 200 corps years. The average number of deaths by horse kick was 121 / 200 = 0.61, which means that
The first column of the table, The Simulating costs of car accidentsThe following question was taken from Probability in with Applications in R by Robert Dobrow. Suppose that the number of accidents per month at a busy intersection in the center of a certain city is 7.5. This event follows a Poisson distribution and Every time an accident occurs at this intersection, the city government has to pay about $25,000 to clean up the area. What is the average cost of these accidents per year? This question is a lot easier than it probably sounds. We know that the average number of accidents per month is 7.5. We also know that there are 12 months in a year, so the average number of accidents per year is just the product of these two numbers. Finally, since we also know the average cost per accident, the average cost of accident clean-up per year for this city is just the product of these three numbers.
In a typical year, this city can expect to pay about $2.25 million in accident clean-up costs for this intersection. One thing that we should remember, however, is that we are talking about a random variable which follows a certain distribution. This means that there will always be some random variation in annual accident costs for this city. To get an idea of how much accident costs can vary, we’re going to run a simulation. First,
we’ll simulate the annual accident cost for one year. We’ll use Next, we’ll multiply each element inside of
In this simulation, the total cost of cleaning up after accidents was about $2.32 million. Now we’re going to use
In this simulation, the mean cost of accident clean-up is about $2.26 million, which is quite close to the theoretical total. This cost is marked on the histogram above with a dashed red line. How big is this town? Is this the most dangerous intersection in terms of accident frequency? How does it compare to others in the town? Unfortunately we can’t answer any of these questions. But spending over $2 million in a typical year to deal with accidents at a single intersection is a sign that something needs to be done about the design of that intersection to decrease the frequency of those accidents because at the very least, they are a drain on the city’s finances. Bomb hits over London during World War 2The following two paragraphs are copied directly from Probability with Applications in R by Robert Dobrow.
The data from this study is shown in the table below.
This table is interpreted in a way similar to the one about horse kicking deaths. The first column represents the number of balls (bombs) that landed in one of the bowls (1/4 km square areas). The second and third columns represent the number of areas in which a certain number of bombs landed and the number of areas in which it was expected that number of bombs would land according to the Poisson distribution, respectively. Like the study about horse kick deaths, the observed and expected values are quite close because the random variable being examined appears to follow a Poisson distribution. While I was looking around the internet to find more information about this dataset and possibly the original data itself, I stumbled upon some important historical details about this study that are worth knowing about so that we properly understand what this data really tells us. Dobrow’s description of this study’s history contains a couple of minor factual errors. William Feller was not the original author of the London bombing study. He did write about it in his 1968 book An Introduction to Probability Theory and Its Applications, Vol. 1, but the passage which covers this topic contains a citation for a 1946 article in an actuarial journal by a different author, R. D. Clarke. This article is linked below. https://www.actuaries.org.uk/system/files/documents/pdf/0481.pdf Also, this data doesn’t cover all of London, but rather only a 144 square kilometer section of the southern part. This is explained in the original article linked above. Finally, the original purpose of the study was to investigate whether or not bombs that were dropped on this part of London landed in clusters or not. That is, were the patterns in which the bombs landed in this part of the city random or not? As the author of the original study explains in his short article, the answer is that there is insufficient evidence to conclude that the bombs landed in clusters as was frequently claimed. Now we’re going to run a simulation with this data that’s based on one by Robert Dobrow. His original script for this simulation is linked below. https://people.carleton.edu/~rdobrow/Probability/R%20Scripts/Chapter%203/Balls.R The first thing we’re going to do is create some variables which match the ones described in the quotes from Dobrow at the beginning of this section. We will use a Now let’s have a glance at our results. Imagine that the printout below is an accurate spatial representation of this section of London. Each one of the numbers below represents one quarter square kilometer section of the area that was targeted and how many bombs landed there. Some places were luckier than others.
We can briefly summarize this data using
How do these simulated totals compared to what we would expect according to the Poisson distribution? Getting all of this data into a summary dataframe will be somewhat complicated, but the process is mostly familiar.
Notice how the theoretical probabilites were calculated. We’ll conclude with a visual summary of our bombing simulation results. The red dashed line is drawn at our value for |