Gaussian statistic Model

Gaussian statistic Model

Gaussians statistic Model Introduction carl ****erick gas aik bacha aur aik shandaar rayazi daan tha jo 18 win sadi ke aakhir se 19 win sadi ke wast tak zindah raha. gas ki shiraakat mein chokor masawaat, kam az kam ka tajzia, aur aam taqseem shaamil thi. agarchay aam taqseem 1700 ki dahai ke awail mein abraham d ki tahreeron se maloom hui thi, lekin is daryaft ka crdt aksar ko diya jata hai, aur aam taqseem ko aksar taqseem kaha jata hai. shumariyat ka ziyada tar mutalea se shuru sun-hwa, aur is ke models ka itlaq maliyati mandiyon, qeematon aur imkanaat par hota hai. jadeed daur ki eslehaath aam taqseem ko ghanti ke munhani khutoot ke tor par mutayyan karti hai, wast aur tagayur ke ke sath. yeh mazmoon ghanti ke munhani khutoot ki wazahat karta hai aur is tasawwur ko tijarat par laago karta hai. pemaiesh ka markaz : ost, aur mood taqseem ke markaz ke iqdamaat mein wast, aur mood shaamil hain. ost, jo ke mehez aik ost hai, tamam askorz ko shaamil karkay aur score ki tadaad se taqseem karkay haasil kya jata hai.order shuda namoonay ke do darmiyani nambaron ko shaamil karkay aur do se taqseem karkay haasil kya jata hai ( data ki qadron ki yaksaa tadaad ki soorat mein ), ya sirf darmiyani qader ( data ki qadron ki taaq tadaad ki soorat mein ) le kar haasil kya jata hai. mood eqdaar ki taqseem mein nambaron mein sab se ziyada baar baar hota hai. ahem take ways gaussian taqseem aik shmaryati tasawwur hai jisay aam taqseem ke naam se bhi jana jata hai. adaad o shumaar ke diye gaye set ke liye, aam taqseem wast ( ya ost ) ko markaz mein rakhti hai aur mayaari inhiraf wast ke ird gird phelao ki pemaiesh karte hain. aam taqseem mein, tamam data ka 68 % ost ke -1 aur + 1 mayaari inhiraf ke darmiyan aata hai, 95 % do mayaari inhiraf mein aata hai, aur 99. 7 % teen mayaari inhiraf mein aata hai. aala mayaari inhiraf wali sarmaya kaari ko kam mayaari inhiraf wali sarmaya kaari ke muqablay mein ziyada khatrah samjha jata hai . Gaussian Model to trading mayaari inhiraf utaar charhao ki pemaiesh karta hai aur is baat ka taayun karta hai ke wapsi ki kis karkardagi ki tawaqqa ki ja sakti hai. chhootey mayaari inhiraf ka matlab sarmaya kaari ke liye kam khatrah hota hai jabkay aala mayaari inhiraf ziyada khatray ka matlab hota hai. tajir ikhtitami qeematon ko ost se farq ke tor par map satke hain. asal qader aur ost ke darmiyan aik bara farq aik aala mayaari inhiraf aur is wajah se ziyada utaar charhao ki tajweez karta hai. woh qeematein jo ost se bohat daur hoti hain woh wapas wast par wapas askati hain, taakay tajir un halaat ka faida utha saken, aur qeematein jo choti range mein tijarat karti hain, break out ke liye tayyar ho sakti hain. mayaari inhiraf ki tijarat ke liye aksar istemaal honay wala takneeki isharay hai kyunkay yeh 21 din ki mutharrak ost ke sath oopri aur nichale bindz ke liye do mayaari inhiraf par mutayyan utaar charhao ka aik pemana hai. skew aur data aam tor par aam taqseem ke ain mutabiq ghanti vicar patteren ki pairwi nahi karta hai. Skew and kurtosis skewness aur kurtosis is baat ke pemana hain ke data is misali namoonay se kaisay hatt jata hai. skewness taqseem ki dam ki ghair mutanasib pemaiesh karta hai : aik misbet tircha data hota hai jo nichale hissay ki nisbat wast ke ounchay hissay par ziyada hatt jata hai. manfi tirchi ke liye is ke bar aks sach hai. jab ke tircha pan dam ke Adam tawazun se mutaliq hai, ka talluq dam ki intahaa se hai chahay woh ost se oopar hon ya neechay. distri byoshn mein misbet izafi hota hai aur adaad o shumaar ki qadren ziyada hoti hain jo ke aam taqseem ki paish goi se kahin ziyada hoti hain ( maslan, ost se paanch ya ziyada mayaari inhiraf ). aik manfi izafi jisay kaha jata hai, intehai qader ke kirdaar ke sath aik aisi taqseem ki khasusiyat hai jo aam taqseem se kam intehai hai. takhfeef aur ke itlaq ke tor par, fixed income sikyortiz ke tajzia ke liye, misaal ke tor par, jab sood ki shrhin mukhtalif hoti hain to kisi port folyo ki utaar charhao ka taayun karne ke liye mohtaat shmaryati tajzia ki zaroorat hoti hai. woh model jo harkat ki simt ki passion goi karte hain inhen band port folyo ki karkardagi ki passion goi karne ke liye tirchi pan aur ka Ansar hona chahiye. un shmaryati tasawurat ko kayi dosray maliyati alaat jaisay stock, ikhtiyarat aur currency ke joron ke liye qeemat ki naqal o harkat ka taayun karne ke liye mazeed laago kya ja sakta hai .

Gaussian Statistics Model: Ek Jaiza
1. Gaussian Statistics Kya Hai?


Gaussian statistics, jise normal distribution bhi kaha jata hai, ek statistical model hai jo data ki distribution ko describe karta hai. Is model ka naam Carl Friedrich Gauss ke naam par rakha gaya hai, jinhone is distribution ki pehchaan ki thi. Ye model natural phenomena, social sciences, aur engineering me mukhtalif data sets ko analyze karne ke liye istamal hota hai.
2. Gaussian Distribution Ki Pehchan


Gaussian distribution ek bell-shaped curve hai, jise normal curve bhi kaha jata hai. Iski khasiyat ye hai ke is mein mean, median, aur mode sab same hote hain. Is curve ka aik center hota hai, jo data ke central tendency ko represent karta hai, jabke iske do tails hote hain jo data ke extreme values ko represent karte hain.
3. Mathematical Representation


Gaussian distribution ko mathematically is formula se represent kiya jata hai: f(x)=1σ2πe−(x−μ)22σ2f(x) = \frac{1}{\sigma \sqrt{2\pi}} e^{-\frac{(x - \mu)^2}{2\sigma^2}}f(x)=σ2π1e−2σ2(x−μ)2 Yahan μ\muμ mean hai, σ\sigmaσ standard deviation hai, aur eee Euler's number hai. Ye formula distribution ki shape aur scale ko define karta hai.
4. Central Limit Theorem


Central Limit Theorem (CLT) Gaussian statistics ki buniyad hai. Is theorem ke mutabiq, agar kisi random variable ke samples ko average kiya jaye to in samples ka mean Gaussian distribution ki taraf jata hai, chahe original distribution kuch bhi ho. Is ka matlab ye hai ke agar hum bohot saare independent random samples lein, to unka average Gaussian distribution ko follow karega.
5. Applications of Gaussian Statistics


Gaussian statistics ka bohot saare fields mein istemal hota hai. Yeh finance mein stock prices ki forecasting, quality control mein manufacturing processes ka analysis, aur medical research mein patient outcomes ki study ke liye istemal hota hai.
6. Descriptive Statistics Aur Gaussian Model


Descriptive statistics mein mean, median, mode, variance, aur standard deviation shamil hote hain. Jab hum Gaussian model ki madad se data ko analyze karte hain, to in statistics ka istemal hota hai. Ye values data ki distribution ki khasiyat ko samajhne mein madad deti hain.
7. Data Visualization


Data ko visualize karna bhi Gaussian statistics ka aik aham hissa hai. Histograms, box plots, aur Q-Q plots data ki distribution ko samajhne ke liye istemal hote hain. In visualizations se hum dekh sakte hain ke data Gaussian distribution ko follow kar raha hai ya nahi.
8. Normalization


Normalization ka process data ko Gaussian distribution ki taraf lekar aata hai. Is process mein data ko scale aur shift kiya jata hai takay wo mean zero aur standard deviation one par aa jaye. Is se data ka analysis aur interpretation asan ho jata hai.
9. Outliers Aur Gaussian Statistics


Gaussian model outliers ko identify karne mein madadgar hota hai. Outliers wo data points hote hain jo baaki data se bohot alag hote hain. Jab hum data ko Gaussian distribution par plot karte hain, to in outliers ko asani se dekh sakte hain.
10. Limitations of Gaussian Statistics


Har data set Gaussian distribution ko follow nahi karta. Kuch data sets skewed hote hain ya unme kurtosis hoti hai, jo Gaussian assumptions ko violate karte hain. Is liye, zaroori hai ke data ko pehle analyze karna chahiye aur dekhna chahiye ke kya wo Gaussian distribution ko follow karta hai ya nahi.
11. Non-Gaussian Distributions


Bohot se aise distributions hain jo Gaussian nahi hote. Inme exponential, Poisson, aur binomial distributions shamil hain. In distributions ka analysis alag statistical techniques aur models ka istemal karke kiya jata hai.
12. Statistical Inference


Statistical inference ka matlab hai data se conclusions nikalna. Gaussian statistics ka istemal hypothesis testing aur confidence intervals banane ke liye hota hai. Ye techniques researchers ko data ki population ke bare mein andaza lagane mein madad karti hain.
13. Software Tools


Aaj kal ke digital daur mein, Gaussian statistics ka analysis karne ke liye kai software tools available hain. R, Python, aur MATLAB jese programming languages mein in statistics ko analyze karne ke liye libraries aur packages available hain. In tools ki madad se researchers aur analysts asani se data ka analysis kar sakte hain.
14. Conclusion


Gaussian statistics model data analysis ka aik powerful tool hai. Iska istemal na sirf academic research mein hota hai, balke industry aur business decision making mein bhi hota hai. Is model ki pehchaan aur understanding se hum data ko behtar tareeqe se samajh sakte hain aur informed decisions le sakte hain. Is tarah, Gaussian statistics data analysis ki duniya mein aik aham maqam rakhta hai.