Exponential Distribution! AWESOME EXPLANATION. Why is it called "Exponential"?
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- เผยแพร่เมื่อ 28 มิ.ย. 2024
- See all my videos at www.zstatistics.com/
0:00 Intro
0:49 Definition
4:41 Visualisation (PDF and CDF)
9:21 Example (with calculations)
17:05 Why is it called "Exponential"??
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This channel is underrated.
All of your videos keep giving me the Eureka moment at some point in the video. Keep doing what you're doing ZED. Lots of love and admiration.
Justin explains exactly what I was wondering about the concept, or the big picture, about Exponential Distribution. I wanted so badly to interpret its graph, but there was no tutorial that told me about it until I reached this video. And this one is amazing! It just enlightens all that I wanted to know about this subject. Thanks a lot, Justin!
Fantastic, zed statistics! This should be the number 1 option for explaining this topic out there! This is awesome (and what learning should be like). Thanks!
Thanks edu boss! Share it round! :)
The best intuitive video on exponential distribution I have seen so far.. Thanks Justin for sharing.
Best I've seen by far
This channel gets me some internel confidence that the topic I am searching for hours on the internet *will* be resolved with more than enough depth with the clarity needed.
your voice so soothing bruh, it plug all the theories into my head perfectly
You seriously rock! I have a test in a few days, and I have watched all of your videos regarding probability distributions. Feeling much much better! Again, thanks so much :)
This video and this channel are definitely the statistics explained in an intuitive way at its best. Love it and feel fortunate to find this resource. THANK YOU!
Over the years, I have searched literally dozens of text books and articles to get an idea why the exponential distribution is a declining curve. This is the first instance that I have encountered a 'success' -- to use a statistical jargon. A similar reasoning explains the exponential smoothing model for forecasting, and only a couple of authors have really bothered to explain it. Great job Justin! Pretty soon, I guess you will need to revise the number of visits to your website!!!!! Thanks a lot!
Wow. Just wow. This video is marvellous! We really appreciate your effort!
The way you explained why the pdf looks like it is really amazing! Thank you! I finally realized exponential is related to binomial distribution!
amazing videos. your explanations, oration, recording, and visuals all are superb!
The best video for understanding exp dist...loved the way it explains!
Thank You so much for the explanation in the "exactly" scenario, zedstatistics. This helped me a lot. Thanks a million.
This is a kind request to have a video series on Permutation, Combination ,Probability and Calculas. I must say your videos are very awesome. The way you explained things is fantastic. Thanks Justin
This video is amazing the only video which explains exponential distribution in depth . Thankyou so much
This really helps me understand how the statistical tests built on these distribution works!
Best intuitive explanation I’ve found. Thanks!
Sir you are sooo kind person, you didn't let us to watch the entire poisson distribution video unlike many youtubers who take advantage of this and make viewers watch multiple videos, Sir you are super. Namaskaram sir🙏🙏🙏🙏🙏
Appreciating your smart way to lead us through exponential distribution
Clearest stats video I have ever watched. Thank you
This video really helped me a lot understanding the difference between Poisson and Exponential distributions. Outstanding ❤ Thank you and keep up the good work 🙏🏻
These videos are incredibly informative ! I encourage you make some more !!!
Great explanation. Cannot be better than that. Crystal clear my concept. Thanks
I think one of the best explanations on Exponential Distribution. Could you please share any content with its link to CTMC and Transient Analysis.
I understand how simple it is just because of your this video. Thank you so much.
Brilliant, loved the simple PDF explanation at the end
Another way to get an intuition for the shape of the exponential distribution would be to draw events on a number line you first draw them equal width apart (if it’s 3 hours per event then draw them one hour apart). Now sample 1 point per hour or something like that, you’ll see that the waiting times follow a uniform distribution. Now we can try to “randomize” the intervals a bit aka move the events around by for example one event 2 hours early and another 2 hours late to balance it out (so that the average rate stays the same). You can see that for the two intervals surrounding the event that’s moved two hours early, they were originally both 3 hours. Then, after the move, they become 1 and 5 hours. For the first interval, all waiting times within 1 hour still remain, on the other hand, higher waiting times between 1 and 3 hours are stripped away and converted to waiting times 3-5 hours in the second intervals. Higher waiting times have a higher chance of being converted to even higher waiting times, but lower waiting times do not. That’s why the density is higher towards shorter waiting times. I hope it makes sense.
Another even simpler way to look at it is: if we sample the waiting times once per hour, for every waiting time of 3 hours, there MUST be one sample each for 2, 1 and 0 hours between it and the next event. On the other hand, if you have a waiting time of 1 hour, there isn’t a guarantee that there exist waiting times higher than 1 hour. In general terms, an instance of a longer waiting time corresponds to one instance each of all the waiting times shorter than it; however, the opposite doesn’t hold true (an instance of a shorter waiting time doesn’t guarantee an instance of any higher waiting time). That’s why the density HAS TO decrease towards higher waiting times.
Awesome. Especially, the last sections explanation was crystal clear. Thank you.
you re video is just perfect. you also explain very well why things are like this or like that
All I can say is Thank you from the bottom of my heart.... This saved me...
Awesome explanation, Sir
Great video thanks for the help!
very very clear explanation. Thank so much. You did help me to understand Possion and Exponential!
Brilliant teacher , very clear with a commonsense approach.
Best explanations ever. Thanks.
Simply superb, thanks for making these videos. Hope you keep making more videos on statistics!
thank you so much for the explanation on exponential distribution i found it easy to understand
Best content for learning statistics for data science
Amazing Class! Salute from Brazil.
Thank u so much!These lectures are very intutive!!
The last part reminds me of the binomial distribution without de combinations in the formula.
Thanks so much! Great video and helpful visuals!
Best channel for Statistics!!!
wow! really good explaination
This was really helpful! Thanks a lot for your kind effort.
Ohh man you made me very clear on exponential distribution thank you so much for it . Also please make a video on Gamma distribution
You are an incredible instructor.
This topic was explained very nicely. Thank you.
Thank you! So easy and clear ❤️🙏🏻
Great explanation! Thank you very much
your explanations are really great. could you do more distrubution videos
Fantastic video. Keep it up.
archangel of stats explanations thx zed
Omg, cant believe this video doesnt have more likes! top level sta video!
You are so good in explaining maths.
so cool, I wondered why distribution looks like that. so clear now!
Thanks a lot. That really is an awesome explanation
Thank you very helpful, can you please do a video on gamma distributions
Wow this is soo coool! It is a great addition to "Practical statistics for data scientists" book. Thanks!
the last few minutes gave the most important intuition! Thanks! 17:05 Why is it called "Exponential"??
Because 0.95 keeps getting multiplied by itself in the function. In other words, it is a constant being raised to a power, which is the nature of an exponential function.
Thank you just soooo much! May the lord give you paradise in this in this one and afterlife.
Hello Sir, I have watched many of your vedios..And I really like those.. Kindly make one vedio on endowgenity. or suggest me some source.
Thank you.🙂
Fantastic explanation.
Fantastic. Keep up your good work!
Did I just learn what exponential distribution is? :)
Thank you!
Saving lives. My lecturer and textbook use lambda as both the Poisson mean and Exponential mean. Can't begin to explain how many hours I wasted not realising they were referring to two different means. Thought I was losing it. Was ready to drop out of math and try my luck in humanities.
just so clear thank you
Great work!
Great explanation man !!!
Sir, thank you so much for the very clear lesson :)
Great class!
Would have been nice to state that the y-axis on the exponential dist is lambda for the PDF and a percentage for the CDF.
Unlike the Poisson Dist as both are in percentage.
This confused me as I wasn't sure what the Y axis meant. I naturally thought percentage and was wondering why nothing was adding up correctly especially at 16:44 - I was like, it should equal 0.025 or 2.5% which is of course wrong. I watched the whole video with the wrong assumption haha
It's mentioned on the y axis, the values. So it's kinda self explanatory 😅
you are right my friend. I had the same doubt throughout the video
- The Y axis on the exponential distribution PDF does not represent Lambda (nor the probability). It actually represents the PROBABILITY DENSITY, which is the RELATIVE LIKELIHOOD of each value on the X axis occurring. It's scale (0 to 3 in this case) is such that the total area under the graph = 1. But you're right that this was not explained at all in the video.
- The Y axis on the exponential CDF and the Poisson distributions is probability, on a scale of 0 to 1, and not percentage, which would have a scale of 0 to 100.
Very good video. Thank you.
Hi, could you make a video about Gamma distribution? Thanks
Amazing video thanks, you helped me a lot
Hi thanks for making these videos, can you make one such video on Kappa values and Weibull distribution
I cannot thank you enough for this video
After seeking around a lot of videos its the only video which shows why its PDF looks the way it looks
Amazing explanation
Many many thanks
The axes on the graphs could do with some explanation...
6:06 On the Poisson distribution PMF graph on the left:
- The X axis represents unique visitors to the website per hour.
- The Y axis represents the probability of each discrete number of people visiting per hour.
On the Exponential distribution PDF graph on the right:
- The X axis represents hours until next arrival.
- The Y axis does NOT represent the probability itself, which would have a scale of 0 to 1. Rather, the Y axis represents the PROBABILITY DENSITY, which is the RELATIVE LIKELIHOOD of each value on the X axis occurring. It's scale (0 to 3 in this case) is such that the total area under the graph = 1.
08:27 - On both CDF graphs, the Y axes DO represent the probability (scale 0 - 1).
10:21 until the end - The Y axis still represents the probability density (converted for minutes) and not the actual probability.
17:10 The explanation is a bit misleading. It doesn't explain why the graph falls; if the Y axis represented the probability of visitors arriving within discrete periods on the X axis, it would fall anyway, in a linear fashion, so that the product of the values on the X and Y axes remained uniform. But it does explain why the graph is CONCAVE, due the exponential nature of the function, and not linear. It's also unfortunate and confusing in this example that the PROBABILITY DENSITY at 0 minutes (0.05) is the same figure as the PROBABILITY that a visitor lands within each minute (0.05). They are not the same thing.
Does it make sense to look at the probability of an event occurring between two points for an exponential distribution?
Thank you very much❤️
Great thank you very much!
very well explained
Thank you so much!
amazing video, I love it
thanks ! very clear
Beautiful. Wow.. Amazing..
Thank you.
Thanks Zeltz.
excellent sir.
Great bro. Great 😊😊👏👏
I always thumps up before watching you're videos :p
Damn that's awesome! Now i understand where the ' exponential' came from.🎉
Hello, First I would like to express my appreciation and admiration for the epic way you're teaching these topics with a big time THANK YOU. I do want to ask this question pertaining to the Poisson requirement that the events must occur at a constant rate paradox. If they're occuring at a constant rate. Does this requirement apply on the average sense? Otherwise, if the rate of events (events per time) is constant, then why are what is the purpose of the distribution?
Thank you!
TH-cam algorithms must be pretty good that it didn’t take me long to find this video on exponential distribution >< This one answered my question exactly which is why the exponential pdf looks like the way it does. Took me to click on 4 different videos and maybe 20mins of watching in total to get to this one